A case study of Cygnus X-1

The GBHC Cyg X-1 has been extensively studied by every major X-ray satellite of the past 30 years, and it has been the focus of extensive theoretical modeling. It spends a large fraction of its time in a spectrally hard, highly variable X-ray state; however, it occasionally transits to a softer, less variable state [265,266,267]. Several such transitions to a soft state have been observed with RXTE [61,62,268]. The geometry within each of these accretion states, as well as the causes of the transitions among the different states, has been the focus of much theoretical speculation and observational study. It is precisely these issues that studies of X-ray lines and reflection features hope to illuminate.

Before discussing the specifics of the line studies, it is worthwhile to review some of the suggested models for the Cyg X-1 system, and to briefly consider their implications for predicted line properties. As Cyg X-1 spends most of its time in the hard state, models have focused on explaining this state. Soon after the discovery of hard state black hole candidates, it was suggested that these spectra were due to Comptonization of soft photons in a hot, low optical depth plasma [135], and such spectra were soon successfully applied to the hard state of Cyg X-1 [136,148]. Comptonization models have invoked, variously, slab geometries (and their variations; see Fig. 6), sphere+disk geometries, and have posited soft seed photons coming from either the optically thick, geometrically thin disk or from synchrotron photons generated within the corona itself.

For the slab or sandwich geometries, it is expected that the generated reflection fraction will be of order unity (half the coronal flux is intercepted by the disk), and thus iron line equivalent widths should also be large ($\sim 200{\rm\thinspace eV}$). If the corona extends inwards toward small disk radii, then relativistic effects will also be prominent. The `pill box' geometry preserves the reflection and line features of this geometry, but reduces the amount of Compton cooling of the corona. `Sphere+disk' geometries were in part specifically considered since, like the pill box, these coronae are less Compton cooled than slab models. In contrast to the pill box models, they also have low reflection fractions ($f\approx0.3$) and produce weak iron line features. The degree to which relativistic effects are prominent in such line features is dependent upon the transition radius between corona and disk. ADAF models essentially adopt the `sphere+disk' geometry; however, their hard spectra tend to be more centrally concentrated, and they often posit large transition radii between inner corona and outer disk. Thus, although not a necessary feature of ADAF models in general, many specific realizations of ADAF models produce very small reflection fractions, as well as very weak and narrow fluorescent iron line features.

The observational nature of the reflection and line features observed in Cyg X-1 has been controversial. In order to illustrate how technology, theoretical prejudice and sociology influence our understanding of such a complex system, we will present a detailed historical account of the iron line in Cyg X-1. The first reported detection of a broad Fe line feature in Cyg X-1 was made by Paul Barr and collaborators using data from the EXOSAT Observatory [200]. The line was seen to be of moderate strength (an equivalent width of 120eV), have a slightly redshifted peak from that of neutral iron (6.2keV, as opposed to 6.4keV), and be fairly broad (Gaussian width of $\sigma = 1.2$keV). This line, however, was not interpreted as indicating a relativistic profile. Instead, it was interpreted as due to Compton scattering in a moderately optically thick ($\tau_{\rm es} \sim 5$), low temperature ($\sim 5$keV) corona. Scattering in such a corona would indeed both broaden and slightly redshift an intrinsically narrow line. It was further hypothesized that the line was predominantly due to recombination radiation in a highly ionized corona, as opposed to being due to fluorescence radiation.

Several years later, however, these exact same observations were reinterpreted as relativistic broadening of a fluorescent line by Andy Fabian and collaborators [189]. In fact, this was the first attempt to claim such a line in any X-ray source. It was noted that, due to the poor intrinsic resolution of EXOSAT in the iron line region ($\Delta E/E> 10\%$), the characteristic ``double horned'' features of relativistic lines would be smeared out, regardless of the inclination, and yield the broad, Gaussian feature previously fit [200]. This interpretation was challenged, however, by prior observations performed with the Tenma X-ray satellite [269]. These observations, carried out in 1983 and spanning several phases of the Cyg X-1 binary orbit, revealed a weaker line (equivalent width 60-80eV) that furthermore was consistent with being somewhat narrower ($\sigma < 1$keV) and being dependent upon orbital phase. This suggested, instead, fluorescence from the surface of the companion (donor) star, not the black hole accretion disk. A broader component emanating from the inner disk regions, however, could not be ruled out by the data.

As we have discussed extensively, a fluorescent iron line is produced along with other spectral signatures -- one also expects to observe the iron K edge, as well as Compton recoiled photons at higher energy. When these features were added to the models of EXOSAT data (as well as to models of earlier HEAO 1-A2 data), Christine Done and collaborators obtained fits that yielded reflection fractions of $\Omega/2\pi \sim 0.5$ and narrow Gaussian lines with equivalent widths $\sim 40$eV [270]. These results were confirmed by observations performed by BBXRT, which was an X-ray telescope with a resolution $E/\Delta E\sim 30$ that was flown aboard the space shuttle in 1990. Specifically, it was found that the inclusion of a reflection component from material with twice the solar abundance of iron obviated the need for anything other than a weak, narrow iron line [271]. This model was then also applied to ASCA data by Ken Ebisawa and collaborators, and, again, when including an iron edge due to reflection, a narrow, weak iron line was found [272, although see the further discussion below].

Unambiguously constraining spectral models that include line features (at 6keV), reflection features (at 10-30keV), and thermal Comptonization features (especially the high energy cut-off at $\approx 100$keV), requires broad band data. Such a data set for Cyg X-1 was obtained in 1991 with a simultaneous Ginga ($\approx2$-30keV) and OSSE ($\approx 50$-1000keV) observation. Ginga, similar to EXOSAT, had poor spectral resolution ($E/\Delta E \approx 10$). Marek Gierlinski and collaborators described these observations [273] with models comprised of low reflection fractions ($\Omega/2\pi =0.2-0.5$), and narrow iron lines with moderate equivalent widths (EW$=90$-140eV). As described in §3.3, there was a growing realization that in order for coronal models to yield very hard spectra with thermal Comptonization cutoffs at very high energy, photon starved geometries were required [144,155,274]. A sphere+disk geometry, for example, could describe the Cyg X-1 data, and furthermore would imply a narrow iron line if the transition between the coronal sphere and the outer thin disk occurred at sufficiently large radius [273,155,274].

It has been the application of more sophisticated coronal and reflection models (with the latter including such effects as ionization of the disk atmosphere and relativistic smearing of the reflection features), coupled with the advent of the new generation of X-ray telescopes (RXTE, BeppoSAX, Chandra, XMM-Newton), that has led researchers to reconsider the possibility of a relativistically broadened iron line in the spectrum of Cyg X-1. An early observation of Cyg X-1 with RXTE by James Dove and collaborators gave ambiguous results in this regard [275]. The spectrum above $\approx 10$keV was extremely well fit by a pure power law with an exponential cutoff, without any signs of spectral curvature associated with Compton recoil photons from a reflection model. Extrapolating the exponentially cutoff power law to energies below 10keV, however, yielded a strong, power law-like excess. This excess could have been produced by three effects: a mismatch in the calibration of spectral slopes between the two instruments that comprise RXTE (PCA and HEXTE; PCA typically yields softer fits than HEXTE to the power-law spectrum of the Crab nebula and pulsar [276]), reflection of a continuum spectrum more complicated than the presumed exponentially cut-off power law, or a combination of an unmodeled soft excess and a strong, broad line. In retrospect, it was likely that all three effects were playing a role in these initial results. The same data, modeled with a sphere+disk coronal model (which included reflection of the Comptonized spectrum with an effective covering fraction of $\Omega/2\pi \approx 0.3$), fit the PCA and HEXTE spectra simultaneously; however, such models yielded strong, broad residuals in the iron line region [275]. At that time, these line-like residuals could not be attributed definitively to a relativistically broadened feature owing to the then poorly known RXTE calibration near energies of $\approx 6$keV [275].

With further improvements to the calibration of the RXTE response in the 6keV region of the spectrum, numerous fits to RXTE observations of Cyg X-1 have continued to indicate strong, broad line features. For one set of (predominantly hard state) RXTE observations of Cyg X-1, Marat Gilfanov and collaborators used a crude Gaussian convolution of a reflection model to simulate relativistic effects [277]. It was found that both the line (equivalent widths $\approx 70$-160eV) and reflection features ($\Omega/2\pi \approx 0.3$-0.7) were well-described by a Gaussian smearing width $\sigma \approx 0.3$-0.9keV. Such large smearing widths would be consistent with relativistic motions and gravitational redshifts in the inner disk.

The EXOSAT, Ginga, and ASCA data were later re-examined by Christine Done and Piotr Zycki with a more complex set of reflection models [278]. Similar to prior analyses [270], these models included reflector ionization using the constant density assumption; however, they also included the effects of relativistic distortions. Furthermore, the models considered a non-relativistic (narrow) set of line/reflection features in conjunction with the relativistically smeared line and reflection features. It was found that all the datasets could be well-fit by models wherein the disk ionization was not very high, and the relativistically smeared line and edge features dominated ($\Omega/2\pi \approx 0.1$-0.2) over the non-relativistic features ($\Omega/2\pi< 0.05$) [278]. Andy Young and collaborators reanalyzed these datasets with an independent model and affirmed the description with a large degree of relativistic smearing of the line and reflection features; however, this latter model postulated a larger reflection fraction ($\Omega/2\pi \approx 1$), albeit with a higher degree of ionization [279].

Analyses of BeppoSAX observations of the Cyg X-1 hard state also were well described by broad line features [280,281]. BeppoSAX had extremely broad energy coverage from $\approx 0.5-200$keV; therefore, it was capable of simultaneously constraining models of the distribution of seed photons for Comptonization (e.g., the disk with temperatures $kT\approx0.1$-2keV), the line/reflection region (6-30keV), and the hard, Comptonized tail (10-200keV). As for the re-analyses of EXOSAT, Ginga, and ASCA data [278], analyses of BeppoSAX by Frontera and collaborators revealed a relativistically smeared reflected power law ($\Omega/2\pi \approx 0.1$-0.3), with the degree of smearing being indicative of the reflection being dominated by the innermost regions of the accretion disk [280]. Similarly, sophisticated Comptonization models, including the effects of (non-relativistic) reflection ($\Omega/2\pi \approx 0.25$), also required the presence of a strong (equivalent width $\approx 350$eV), relativistically broadened line [281].

One can see that there has been something of a split, with the prevailing wisdom prior to 1997 being dominated by the ``narrow'' features point of view, while the prevailing wisdom post-1997 seems to be dominated by the ``broad'', i.e., relativistic, features point of view (with some researchers having been on both sides of the issue). Has this shift been one of sociology, improved theoretical modeling, improved observational data, or some other effects? Improved models have certainly played an important role. For example, in order to explain the ASCA data at the lowest energies, Ken Ebisawa and collaborators invoked a broken power law (with a softer, i.e. steeper, low energy slope and a break energy at $\approx 4$keV) in addition to the disk component with peak temperature of $kT \approx 150$keV [272]. The presence of such a low energy ``soft excess'' (above the requirements of the disk component) in the spectrum of Cyg X-1, as well as other hard state black hole spectra, continues to be debated [278,280,281]. It has been argued, however, that the apparent hardening at energies above 4keV in fact might be due to the red tail of the relativistically broadened iron line [52]. The combination of simultaneous broad band data with models that attempt to (at least somewhat self consistently) model this entire range leaves less leeway to introduce phenomenological model components (e.g., a spectral break at 4keV) that might remove evidence of a relativistically broadened line. It is worthwhile noting that Comptonization models [275,281] seem to require the broad line, even when including the other effects of reflection.

The above discussion highlights the complexity inherent in stellar mass black hole spectra. Unlike the case of AGN, it is clear that a simple, exponentially cutoff power law is insufficient to adequately describe the underlying X-ray continuum. This is especially true at soft energies, as the hottest GBHC accretion disks ($kT \approx 2$keV) can have significant spectral contributions into the red tail region of any broadened iron line. A further complication arises from the fact that stellar mass black hole disks likely represent a wide range of disk inclinations. It is typically thought that Seyfert 1 disks are viewed reasonably close to face-on (see Fig. 4); therefore, the gravitational redshift and transverse Doppler shifts typically cause the blue wing of a broadened K$\alpha$ line to lie at energies below its associated ionization edge. This is not the case with potentially more highly inclined stellar mass black hole systems. There, especially if one misidentifies the continuum power law slope, it is much easier to mis-model the blue wing of such a line with a reflection edge.

Figure 18: Ratio of RXTE observations of GX339$-$4 to RXTE observations of the Crab nebula and pulsar, normalized to unity at 10keV. The spectrum of the Crab nebula is widely believed to be a featureless power-law continuum. Showing the observations this way gives an indication of the intrinsic resolution of the detectors, as well as minimizes the worry that the line features are artifact of a poorly determined detector response. Note that despite the fact that these two observations have nearly identical fluxes and average spectral slopes, their line profiles are different.

Most importantly, due to their extremely short viscous and thermal time scales (compared to AGN), the environment of the accretion flow in a stellar mass black hole system can be very different from observation to observation. The existence of ``state changes'' clearly points toward this; however, even within a given state large changes in the spectral properties are observed [282,277,283, for example]. Thus, some of the seemingly different results quoted above are undoubtedly due to changes in the structure of the accretion flow between observations (e.g., changes in the ionization state, the disk inclination to our line of site, the disk/corona geometry, etc.). These changes, in fact, can be sometimes associated solely with the line profile. As an example, in Fig. 18 we show two RXTE-PCA observations of the stellar mass black hole candidate GX339$-$4 in its hard state [52]. To minimize features due to uncertainties in the calibration and response of RXTE, the data are presented as a ratio to RXTE observations of the Crab nebula and pulsar (which are thought to possess a synchrotron hard X-ray spectrum well approximated by a featureless power-law). Even though these two observations represent nearly the same flux, power law slope, and (low) fitted reflection fraction, one exhibits a broad line residual, while the other one exhibits a line residual consistent with being narrow.

Figure 19: Simultaneous Chandra and RXTE observation of Cygnus X-1, fit with a simple power law model (J. Miller, priv. comm.; see also [284]). The Chandra data have been rebinned to show both the narrow core at 6.4keV, as well as the broad component. The broad component in Chandra agrees well with that seen in RXTE. RXTE data further show an upturn at high energy likely due to reflection.

A final important example of spectral variability in stellar mass black hole systems is that due to orbital variation. A binary orbital dependence for the strength of the iron line has been previously reported for Cyg X-1, which was taken as evidence that the line was due to fluorescence by the secondary, not by the relativistic regions of the inner disk [269]. Recent Chandra observations, however, have dramatically demonstrated that the line region in fact is comprised of both narrow and broad components [284,285]. For the first time, instruments exist with high enough spectral resolution to definitively resolve the narrow component of the line; however, as shown by Jon Miller and collaborators, the Chandra sensitivity and energy coverage also convincingly reveal the broad component of the line. In Fig. 19 we show the profile, comprised of both narrow and broad features, obtained with the Chandra observations performed by Miller et al. Further Chandra observations reveal that the the narrow line component is not always present in the data (H. Marshall 2001, priv. comm.; see also [286]). The narrow line has an equivalent width of only 80eV, while the parameters of the broad line component (equivalent width $\approx 140$eV) agree well with those previously found with, e.g., RXTE observations [284]. Thus, whereas the presence of a (variable) narrow line component complicates analyses performed with broader resolution instruments, it apparently does not obviate the need for a broad line to be present.

All of the above observations refer to spectrally hard states (often called ``low'' to ``intermediate'' states); however, Cyg X-1 occasionally transits into a much softer state (often called a ``high state''). Although rarer, observations of this soft state have been performed with ASCA, RXTE, BeppoSAX [62,287,288,277,281], and more recently Chandra. All of the above caveats about determining line profiles in the hard state apply to the soft state as well. We further note that due to the increased strength and temperature of the soft ``disk'' component (with maximum temperature $kT \approx 300$eV), continuum modeling near the red wing of the line region is even more difficult. Given these caveats, however, several researchers have claimed increased reflection fractions ($\Omega/2\pi \approx 0.6$-1.5), and increased line widths ($\sigma \approx 1$-2keV), for moderately strong lines (equivalent widths $\approx 80$-190eV) [288,281]. There have even been claims for evidence that the line energy increases to $\approx 6.7$keV, i.e., consistent with heavily ionized Fe, in the soft state [62].