CHANDRA X-RAY SPECTROSCOPY OF THE FOCUSED WIND IN THE CYG X-1 SYSTEM.    I.

# Chandra X-ray spectroscopy of the focused wind in the Cygnus X-1 system I. The nondip spectrum in the low/hard state

## Abstract

We present analyses of a 50 ks observation of the supergiant X-ray binary system Cygnus X-1/HDE 226868 taken with the Chandra High Energy Transmission Grating Spectrometer (HETGS). Cyg X-1 was in its spectrally hard state and the observation was performed during superior conjunction of the black hole, allowing for the spectroscopic analysis of the accreted stellar wind along the line of sight. A significant part of the observation covers X-ray dips as commonly observed for Cyg X-1 at this orbital phase, however, here we analyze only the high count rate nondip spectrum. The full 0.5–10 keV continuum can be described by a single model consisting of a disk, a narrow and a relativistically broadened Fe K line, and a power-law component, which is consistent with simultaneous RXTE broad band data. We detect absorption edges from overabundant neutral O, Ne, and Fe, and absorption line series from highly ionized ions and infer column densities and Doppler shifts. With emission lines of He-like Mg xi, we detect two plasma components with velocities and densities consistent with the base of the spherical wind and a focused wind. A simple simulation of the photoionization zone suggests that large parts of the spherical wind outside of the focused stream are completely ionized, which is consistent with the low velocities (200 km s) observed in the absorption lines, as the position of absorbers in a spherical wind at low projected velocity is well constrained. Our observations provide input for models that couple the wind activity of HDE 226868 to the properties of the accretion flow onto the black hole.

accretion, accretion disks – stars: individual (HDE 226868, Cyg X-1) – stars: winds, outflows – techniques: spectroscopic – X-rays: binaries
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## 1. Introduction

Cygnus X-1 (catalog Cygnus X-1) was discovered in 1964 (Bowyer et al. 1965) and soon identified as a high-mass X-ray binary system (HMXB) with an orbital period of 5.6 d (Murdin & Webster 1971; Webster & Murdin 1972; Bolton 1972). It consists of the supergiant O9.7 star HDE 226868 (catalog HDE 226868) (Walborn 1973; Humphreys 1978) and a compact object, which is dynamically constrained to be a black hole (Gies & Bolton 1982). The detailed spectroscopic analysis of HDE 226868 by Herrero et al. (1995) gives a stellar mass , leading to a mass of 10  for the black hole, if an inclination is assumed. Note that Ziółkowski (2005) derives a mass of from the evolutionary state of HDE 226868, corresponding to , while Shaposhnikov & Titarchuk (2007) claim from X-ray spectral-timing relations.

Cyg X-1 is usually found in one of the two states that are distinguished by the soft X-ray luminosity and spectral shape, the timing properties, and the radio flux (see, e.g., Pottschmidt et al. 2003; Gleissner et al. 2004a, b; Wilms et al. 2006): the low/hard state is characterized by a lower luminosity below 10 keV, a hard Comptonization power-law spectrum (photon index ) with a cutoff at high energies (folding energy keV) and strong variability of 30% root mean square (rms). Radio emission is detected at the 15 mJy level. In the high/soft state, the soft X-ray spectrum is dominated by a bright and much less variable (only few % rms) thermal disk component, and the source is invisible in the radio. Within the classification of Remillard & McClintock (2006), the high/soft state of Cyg X-1 corresponds to the steep power-law state rather than to the thermal state, as a power-law spectrum with photon index may extend up to 10 MeV (Zhang et al. 1997; McConnell et al. 2002; Cadolle Bel et al. 2006). Most of the time, Cyg X-1 is found in the hard state, but transitions to the soft state and back after a few weeks or months are common every few years. Transitional or intermediate states (Belloni et al. 1996) are often accompanied by radio and/or X-ray flares. Similar to a transition to the soft state, the spectrum softens during these flares and the variability is reduced. This behavior is called a “failed state transition” if the true soft state is not reached (Pottschmidt et al. 2000, 2003). Transitional states have occurred more frequently since mid-1999 than before (Wilms et al. 2006), which might indicate changes in the mass-accretion rate due to a slight expansion of HDE 226868 (Karitskaya et al. 2006).

HMXBs are believed to be powered by accretion from the stellar wind. The accretion rate and therefore X-ray luminosity and spectral state are thus very sensitive to the wind’s detailed properties such as velocity, density, and ionization. For HDE 226868, Gies et al. (2003) found an anticorrelation between the H equivalent width (an indicator for the wind mass loss rate ) and the X-ray flux. Considering the photoionization of the wind would allow for a self-consistent explanation (see, e.g., Blondin 1994): a lower mass loss gives a lower wind density and therefore higher degree of ionization due to the irradiation of hard X-rays, which reduces the driving force of HDE 226868’s UV photons on the wind and results in a lower wind velocity , leading finally to a higher accretion rate (, Bondi & Hoyle 1944). However, Gies et al. (2008) find suggestions that the photoionization and velocity of the wind might be similar during both hard and soft states. UV observations allow the photoionization in the HDE 226868 / Cyg X-1 system to be probed: Vrtilek et al. (2008) reported P Cygni profiles of N v, C iv, and Si iv with weaker absorption components at orbital phase , i.e., when the black hole is in the foreground of the supergiant. This reduced absorption, which was already found by Treves et al. (1980), is due to the Hatchett & McCray (1977) effect, showing that those ions become superionized by the X-ray source. Gies et al. (2008) model the orbital variations of the UV lines assuming that the wind of HDE 226868 is restricted to the shadow wind from the shielded side of the stellar surface (Blondin 1994), i.e., the Strömgren (1939) zone of Cyg X-1 extends to the donor star. However, this assumption applies only to the spherical part of the wind, which might therefore hardly contribute to the mass accretion of Cyg X-1.

As HDE 226868 is close to filling its Roche lobe (Conti 1978; Gies & Bolton 1986a, b), the wind is not spherically symmetrical as for isolated stars, but strongly enhanced toward the black hole (“focused wind”; Friend & Castor 1982). The strongest wind absorption lines in the optical are therefore observed at the conjunction phases (Gies et al. 2003). Similarly, X-ray absorption dips occur preferentially around , i.e., during superior conjunction of the black hole (Bałucińska-Church et al. 2000). These dips are probably caused by dense, neutral clumps, formed in the focused wind where the photoionization is reduced, although recent analyses have also suggested that part of the dipping activity may result from the interaction of the focused wind with the edge of the accretion disk (Poutanen et al. 2008).

The photoionization and dynamics of both the spherical and focused winds can also be investigated with the high-resolution grating spectrometers of the modern X-ray observatories Chandra or XMM-Newton. As none of the previously reported observations of Cyg X-1 was performed at orbital phase and in the hard state, when the wind is probably denser and less ionized than in the soft state, the Chandra observation presented here allows for the most detailed investigation of the focused wind to date.

The remainder of this paper is organized as follows: in Section 2, we describe our observations of Cyg X-1 with Chandra and the Rossi X-Ray Timing Explorer (RXTE), and how we model CCD pile-up for the Chandra-HETGS data. We present our investigations in Section 3: after investigating the light curves, we model the nondip continuum and analyze neutral absorption edges and absorption lines from the highly ionized stellar wind – and the few emission lines from He-like ions, which indicate two plasma components. In Section 4, we discuss models for the stellar wind and the photoionization zone. We summarize our results after comparing them with those of the previous Chandra observations of Cyg X-1.

## 2. Observation and Data Reduction

### 2.1. Chandra ACIS-S/HETGS Observation

Cyg X-1 was observed on 2003 April 19 and 20 by the Chandra X-Ray Observatory, see Table 1. An overview on all its instruments is given by the Proposers’ Observatory Guide (CXC 2006). In the first four months of 2003, the RXTE All-Sky Monitor (ASM; see Doty 1994; Levine et al. 1996) showed the source’s 1.5–12 keV count rate to be generally below 50 ASM-cps (Figure 1). At the time of our Chandra observation, it was less than 25 cps (0.33 Crab), typically indicative of the source being in its low/hard state (Wilms et al. 2006).

The High Energy Transmission Grating Spectrometer (HETGS), containing high and medium energy gratings (HEG/MEG; see Canizares et al. 2005) was used to disperse X-ray spectra with the highest resolution (CXC 2006, Table 8.1):

As only half of the spectroscopy array of the Advanced CCD Imaging Spectrometer (ACIS-S; see Garmire et al. 2003), namely a 512 pixel broad subarray, was operated in the timed event (TE) mode, the six CCDs could be read out after exposure times of s and the position of each event is well determined. Photons from the different gratings can thus easily be distinguished due to the different dispersion directions of the HEG and the MEG. Even in its low state, however, Cyg X-1 is so bright that several photons may pile up in a CCD pixel during one readout frame. Both events cannot be discriminated and are interpreted as a single photon with larger energy. As the undispersed image would have been completely piled up, only 10% of those events in a pixel window have been transmitted in order to save telemetry capacity. The first-order spectra are, however, only moderately affected, which can be modeled very well (Section 2.2). The alternative to this approach would have been to use the continuous clocking (CC) mode, where the ACIS chips are read out continuously in 2.85 ms, but only the position perpendicular to the readout direction can be determined for every photon event. The CC mode was, however, avoided due to difficulties in the reconstruction of HEG and MEG spectra and other calibration issues.

The undispersed position of the source is required for the wavelength calibration of the spectra. We redetermined it to , from the intersection of the HEG and MEG arm and the readout streak (Ishibashi 2006). Afterward, the event lists were reduced using the standard software from the Chandra X-ray Center (CXC), CIAO 3.3 with CALDB 3.2.3.17 Exceptionally narrow extraction regions had to be chosen as the background spectrum would otherwise have been dominated by the dispersed extended X-ray-scattering halo around the source (Xiang et al. 2005). The further analysis was performed with the Interactive Spectral Interpretation System (ISIS) 1.4.9 (Houck 2002).18

We use the four first-order MEG and HEG spectra (with two dispersion directions each, called and in the following) which provide the best signal-to-noise ratio (S/N). The “second-order spectra” are dominantly formed by piled first-order events which reach the other order sorting window of data extraction (defined in dispersion-energy space) when the energy of two first-order photons accumulates. This effect is most evident for the MEG, whose even dispersion orders are suppressed by construction of the grating bars (CXC 2006).

### 2.2. Model for Pile-Up in Grating Observations

For the first-order spectra, pile-up causes a pure reduction of count rate: a multiple event, i.e., the detection of more than one photon in a CCD pixel during one readout time, which cannot be separated, is either rejected by grade selection during the data processing or migrates to a higher-order spectrum. The Poisson probability for single events in a pixel event-detection cell (see Davis 2002, 2003; CXC 2005) is

 P1(i)=Λ(i)⋅exp(−Λ(i)), (2)

where the expected number of events, , is given by the total spectral count rate, , at this position (in units of counts per Å and s), and where the constant is

 γ0=3Δλ⋅tframe, (3)

where is the resolution of the spectrometer of Equation (1), and is the frame time. We therefore describe the pile-up in the first-order spectra with the nonlinear convolution model simple_gpile2 in ISIS,19 which exponentially reduces the predicted count rate according to Equation (2):

 C′(λ)=C(λ)⋅exp(−γ⋅Ctot(λ)) (4)

Here, the scale is left as fit parameter, and also takes the photons into account which are dispersed in a higher order . The count rates are estimated from the corresponding effective areas and the assumed photon flux :

 Ctot(λ)=∑3m=1Am(λ/m)⋅S(λ/m) (5)

simple_gpile2 is based on the simple_gpile model (CXC 2005; Nowak et al. 2008), which parameterizes the strength of pile-up by the (maximum) pile-up fraction , while using the parameter of simple_gpile2 avoids to have a nonlocal model which depends on the flux at the position of the highest pile-up.

The effect of pile-up is stronger in the MEG spectra than in the HEG spectra due to the lower dispersion and higher effective area of the MEG. The apparent flux reduction is most significant near 2 keV where the spectrometer has the largest efficiency and the highest count rates are obtained (see Figure 2). It can, however, excellently be modeled with simple_gpile2. When fitting a spectrum, there is always a strong correlation between the pile-up scale and the corresponding flux normalization factor, e.g., the relative cross-calibration factor introduced in Section 3.2. The best-fit values for the pile-up scales found in our data analysis (see Table 2) are only slightly larger than expected from Equation (3) (namely sÅ and sÅ), and the calibration factors are consistent with 1, except for the HEG spectrum, for which both the largest and were found. Given the presence of the correlation, we consider the latter to be a numerical artifact.

According to the simple_gpile2 model, the MEG+1 spectra suffer from 30 % pile-up for Å, peaking at in the Si xiii f emission line at 6.74 Å. Except for some emission lines, among them the Fe K line, the continuum pile-up fraction of the HEG spectra is below 17 %. For the HEG+1 spectrum, the reduction is less than 10 % outside the ranges Å and Å.

### 2.3. Rxte Observation

While Chandra’s HETGS provides a high spectral resolution, the energy range covered is rather limited. Within the framework of our RXTE monitoring campaign, the broadband spectrum of Cyg X-1 was measured regularly, i.e., at least biweekly, since 1998 (see Wilms et al. 2006, and references therein). The observation on 2004 April 19 was extended to provide hard X-ray data simultaneously with the Chandra observation. More than one day was covered by 17 RXTE orbits of 47 min good time, interrupted by 49 min intervals when Cyg X-1 was not observable due to Earth occultations or passages through the South Atlantic Anomaly (SAA), see Figure 3.

Data in the 4–20 keV range from the Proportional Counter Array (PCA; Jahoda et al. 1996) and in the 20–250 keV range from the High Energy X-Ray Timing Experiment (HEXTE; Gruber et al. 1996) were used. The data were extracted using HEASOFT 6.3.1,20 following standard data screening procedures as recommended by the RXTE Guest Observer Facility. Data were only used if taken more than 30 minutes away from the SAA. For the PCA, only data taken in the top layer of the proportional counter were included in the final spectrum, and no additional systematic error was added to the spectrum. During the observation, different sets of Proportional Counter Units (PCUs) were operative. During the 11th orbit, extensively used in this work, PCUs 1 and 4 were off.

## 3. Analysis

### 3.1. Light Curve

The Chandra observation covers a phase range between 0.93 and 0.03 in the 5.599829 d binary orbit (Gies et al. 2003, whose epoch is HJD ). The top panel of Figure 4 shows the light curve of first-order events (MEG1, HEG) in the full band accessible with Chandra-HETGS. During several dip events, the flux is considerably reduced. The absorption dips distinguish themselves also by spectral hardening (the bottom panel of Figure 4). We extract a 16.1 ks nondip spectrum, which is the subject of this paper, from all times when the total count rate exceeds 82.7 cps; these are indicated by dark points in Figure 4. The analysis of dip spectra will be described in a subsequent paper.

The RXTE light curve shows considerable variability as well. Although the dips are more obviously detected with Chandra in the soft X-ray band, similar structures are also seen with RXTE-PCA or even -HEXTE, especially in the last RXTE orbits of these observations (Figure 3). We chose to infer the nondip broadband spectrum from the RXTE data taken during the 11th orbit, which was performed entirely during the first part of the nondip phase. Other parts are interrupted by dips, occultations, or have nonuniform PCU configuration.

### 3.2. Continuum Spectrum

The broadband spectrum of Cyg X-1 in the hard state can be described by a broken power-law with exponential cutoff (Figure 5). Since the parameters of this phenomenological model are correlated with those of physical Comptonization models (see, e.g., Wilms et al. 2006, Fig. 11), we are justified in using the aforementioned simple continuum model for this paper focusing on the spectroscopy of the wind. We describe the whole 0.5–250 keV spectrum consistently with one broken power-law model, i.e., there is no need to fit the continuum locally.

Taking pile-up into account (Section 2.2), the nondip Chandra spectra alone can already be described quite well by a weakly absorbed, relatively flat power-law spectrum with a photon index (Table 2). This result is consistent with the fact that the break energy of the broadband broken power-law spectrum is found at keV, i.e., the Chandra data are virtually entirely in the regime of the (steeper) photon index . The onset of the exponential cutoff (with folding energy ) is at keV and thus also well above the spectral range of Chandra. As it is known that there are cross-calibration uncertainties between Chandra and RXTE (Kirsch et al. 2005), we use constant factors for the relative flux calibration of every spectrum and also separate parameters (HETGS) and (PCA), for which we find similar values within the joint model (see Table 2). In order to describe a weak soft excess, we add a thermal disk component, which accounts for 9 % of the unabsorbed 0.5–10 keV flux. The disk has a color temperature of keV; similar to that found by Makishima et al. (2008) and Bałucińska-Church et al. (1995), who described the soft excess with a  keV blackbody only, but the temperature may be too high by a factor (Shimura & Takahara 1995). The norm parameter of the diskbb model is

where is the distance and is the inclination of the disk, which can deviate from the orbital inclination (Herrero et al. 1995) as the disk may be precessing with a tilt (Brocksopp et al. 1999). is related to the inner radius of the disk, (with and ; Merloni et al. 2000). In spite of these uncertainties and the large statistical error of (more than 50 %), the inner disk radius can be estimated to if a distance kpc (Ninkov et al. 1987a) and a Schwarzschild radius km (Herrero et al. 1995) are assumed. Thus, the disk is consistent with extending close to the innermost stable circular orbit (ISCO).

The good S/N afforded by the RXTE-PCA data clearly reveals an iron fluorescence K line. While the instrumental response of the proportional counters does not allow for a resolution of the line profile details, i.e., whether it is narrow or relativistically broadened, the Chandra-HEG spectra (Figure 6) do resolve a strong narrow component at 6.4 keV. Nevertheless, since the integrated flux of the Chandra measured line is insufficient to account for all of the PCA residuals in this region, we include an additional broad feature to our modeling, which is also compatible with the Chandra spectrum. Given the relatively low S/N at these energies, we do not model the broad iron line with a proper physical model such as a relativistically broadened line, but use a Gaussian with its energy fixed at 6.4 keV, as the latter is hardly constrained by the data. These results illustrate the synergy of the simultaneous observation with complementary instruments, as the combination of narrow and broad line could only be revealed by the analysis with a joint model.

Our global model for the continuum spectrum now enables us to address the features of the high-resolution Chandra spectra, which is the topic in the remainder of this section.

### 3.3. Neutral Absorption

Absorbing columns can be measured most accurately from the discrete edges in high-resolution spectra at the ionization thresholds. We detect the most prominent L-shell absorption edge of iron and the K-shell absorption edges of oxygen and neon. Juett et al. (2004, 2006a) have inferred the fine structure at those edges from earlier Chandra-HETGS observations of Cyg X-1 and other bright X-ray binaries: the Fe L and L edges, due to the ionization of a 2p or a 2p electron, respectively, are separately detectable at 17.2 Å and 17.5 Å. The O K-edge at 22.8 Å is accompanied by (1s2p) K and higher (sp) resonance absorption lines. The K line occurs at 23.5 Å for neutral O i and at lower wavelengths for ionized oxygen. In the case of neon, neutral atoms have closed L-shells, such that Ne i only shows a (1s3p) K absorption line close to the K-edge at 14.3 Å, while ionized neon also shows K absorption lines, e.g., Ne ii at 14.6 Å and Ne iii at 14.5 Å. Improved modeling of the neutral absorption that takes these features into account has recently been included in the photoabsorption model tbnew24 (Juett et al. 2006b), an extension of the commonly used tbvarabs model (Wilms et al. 2000).

As part of the spectral model for the whole continuum, the tbnew model can be used to describe the absorption edges detected with the Chandra observation of Cyg X-1 discussed in this paper. Figure 9 shows the Fe L-edges requiring a blueshift by km s of the tbnew model, which relies on the cross sections of metallic iron measured by Kortright & Kim (2000). Unlike Schulz et al. (2002), Miller et al. (2005) and Juett et al. (2006a) have also found that the Fe L edge requires a small shift; their mean position of maximum optical depth is Å, but our value Å is still lower. The shift could be caused by the Doppler effect due to a moving absorber, by a modified ionization threshold due to chemical bonds, or ionization of the iron atoms (van Aken & Liebscher 2002). In an analysis of the Cyg X-1 high/soft and low/hard state, focused on this spectral region, J. Lee et al. (2008, in preparation) find that the Fe L-edges here can likely be modeled by a heterogeneous combination of gas and condensed matter of iron in combination with oxygen local to the source environment. If, as suggested by these authors, the magnitude of the shift is due to molecules and/or dust, this shift is one identifying signature of the composition and charge state of the condensed state material. Such direct Chandra X-ray spectroscopic detection of dust via its associated edge structure was first suggested for observations of the Fe L-edge in the active galactic nucleus MCG6-30-15 (Lee et al. 2001) and for the observations of the Si K-edge in the microquasar GRS 1915+105 (Lee et al. 2002). The latter study associated the observed Si K-edge structure with SiO, although the origin – source environment or Chandra CCD gate structure – was unclear in this case.

The blueshift of km s which has been determined for all other absorption edges is consistent with zero. The O K-edge can only be seen in the MEG spectra after heavy rebinning (Figure 9). Nevertheless, the K resonance absorption line of O i is clearly detected. The region around the Ne edge (Figure 9) is dominated by Fe xviii absorption lines, possibly blending with the K absorption lines of Ne ii and Ne iii. No other strong edges are clearly visible in the spectrum. The Na K-edge (at 11.5 Å; Verner & Yakovlev 1995) blends with an absorption line due to the 2s3p excitation of Fe xxii. The Mg K-edge (at 9.5 Å) blends with the Ne x Ly  absorption line. The Si K-edge (at 6.7 Å) is strongly affected by pile-up and blends with the Mg xii Ly  absorption line. The S K-edge (at 5.0 Å) is relatively weak. Neutral absorption from these elements is nevertheless required within the tbnew model.

The results for the individual abundances, , and resulting column densities, , are presented in Table 3. The alpha process elements O, Ne, Mg, Si, and S are overabundant with respect to the interstellar medium (ISM) abundances as summarized by Wilms et al. (2000) and therefore suggest an origin in the system itself. The total column densities are also compared with the values obtained by Schulz et al. (2002) and Juett et al. (2004, 2006a) from other Chandra observations of Cyg X-1. Table 3 includes the corresponding source luminosities if they are reported in the literature (see also Section 4.4). The X-ray flux was highest during the soft state observation with the observation identification (ObsID) 3724. The column densities confirm the conjecture of Juett et al. (2004) that a higher (soft) X-ray flux ionizes material local to the Cyg X-1 system and reduces the neutral abundances.

The inferred hydrogen column density (see Table 2) is in very good agreement with that from ASCA observations during the soft state in 1996, namely cm (Dotani et al. 1997), and also with obtained from two other different Chandra observations (Schulz et al. 2002; Miller et al. 2002, see also Section 4.4). We note that the large column density toward Cyg X-1 found by many online tools, cm, is obtained from a coarse grid – with (0.675 deg) pixel size – of measurements at 21 cm (Kalberla et al. 2005), which does not resolve the strong variations of in the region around Cyg X-1 (Russell et al. 2007).

### 3.4. Absorption Lines of H- and He-Like Ions

The high-resolution spectra reveal a large number of absorption lines of highly ionized ions. The 1.5–15 Å range is shown in Figure 10 as the ratio between the data and the continuum-model. As the line profiles are not fully resolved, we model each line with a Gaussian profile . In terms of the continuum flux model, , the global model reads

 F(λ)=e−τ(λ)⋅Fcont(λ)=[1+∑lGl(λ)]⋅Fcont(λ). (7)

From a Gaussian’s centroid wavelength and the rest wavelength  of the identified line, the radial velocity

 v=(λ−λ0)/λ0⋅c (8)

of the corresponding absorber can be inferred. With the definition in Equation (7), the norm of is just the equivalent width:

 Wλ,l:=∫[1−Fl(λ)/Fcont(λ)]dλ=∫Gl(λ)dλ (9)

is related to the absorber’s column density, as a bound–bound transition (with the rest frequency and oscillator strength ) in an absorbing plasma with column density creates the following line profile (see Mihalas 1978, Section9-2):

 e−τ(ν)=exp{−Nifij√πe2mecΔνDH(Γ4πΔνD,ν−ν0ΔνD)} (10)

Assuming pure radiation damping, the damping constant equals the Einstein coefficient . The Doppler broadening is given by , i.e., is due to the thermal and turbulent velocities of the plasma. For optically thin lines (with ), the equivalent width is independent of , such that the absorbing column density can be inferred (Spitzer 1978, Eq. 3-48; Mihalas 1978, §10-3):

 (11)

If the lines are, however, saturated, depends on as well, and one has to construct the full “curve of growth” with several lines from a common ground state in order to constrain  (see, e.g., Kotani et al. 2000).

We have therefore performed a systematic analysis of absorption line series: H-like ions are detected by their Lyman series and He-like ions by their resonance absorption series, see Table 4. For those lines that are clearly detected and not obviously affected by blends, the measured velocity shifts (Equation 8) are shown in Table 5. Most of the lines are detected at rather low projected velocity (200 km s). Note that the systemic velocity of Cyg X-1/HDE 226868 is  km s (Gies et al. 2003), and that the radial velocity of both the supergiant and the black hole vanishes at orbital phase , while the radial component of the focused stream should be maximal (likely to be up to 720 km s, see Section 4.1). The column densities in Table 6 are calculated using Equation (11), assuming that the line is on the linear part of the curve of growth. As the strongest lines are, however, often saturated, Equation (11) predicts too small column densities from them. For weak lines, however, the equivalent width is most likely to be overestimated such that the quoted values may rather be upper limits. The properties of the lines (Einstein -coefficients and quantum multiplicities, which determine the oscillator strength, as well as the rest wavelengths) are taken from Verner et al. (1996) and atomdb30 version 1.3.1.

### 3.5. Line Series of H-/He-Like and Fe L-Shell Ions

As an alternative to the curve of growth, we chose to develop a model which implements the expected line profiles (Equation 10) directly for all transitions of a series from a common ground state . The model contains , , and the systemic shift velocity (Equation 8) as fit parameters, and thus avoids the use of equivalent widths at all. This approach allows for a systematic treatment of the iron L-shell transitions as well, which are often blended with other lines such that the different contributions to a line’s equivalent width can hardly be separated when only single Gaussians are used. As an example, Figure 11 shows the Fe xix complex between 12.8 Å and 14 Å. Lines from different Fe xix transitions overlap, and so does the strong Ne ix r-line. Furthermore, the absorption features are often rather weak and no prominent lines can be fitted, whereas the line series model can still be applied. Although a disadvantage of this approach is the larger computational effort, it usually allows us to constrain the parameters of a line series more tightly.

The model with physical absorption line series fits the data hardly worse than the model with single Gaussian lines: of 12812 instead of 12180 before (see Table 2) is obtained. The results are presented in the last row for the whole Ly/He series of Tables 5 and 6 for the H-/He-like ions, and in Table 7 for the Fe L-shell ions. The column densities inferred from the series model are generally in good agreement with the values derived from the single Gaussian fits for the higher transitions of H- or He-like ions (Table 6), while the – sometimes even – lines are saturated. These measurements can be used as input for wind or photoionization models, although a few columns are rather badly constrained if the thermal velocity is left as a free parameter. As the line profiles are not resolved, there is a degeneracy between Doppler-broadened lines and narrow, but saturated lines. The notable fact that no strong wavelength shifts are observed is, however, independent of this degeneracy: almost all line series are consistent with a velocity between  km s and +200 km s. Lower ionization stages of the same element are usually seen at higher blueshift, like in the sequence Fe xxiiixxiixxixx.

### 3.6. Emission Lines from He-Like Ions

The transitions between the 1s ground state and the 1s2s or 1s2p excited states of He-like ions lead to the triplet of forbidden (f), intercombination (i), and resonance (r) line, see Table 4. These lines provide a density and temperature diagnostics of an emitting plasma via the ratios f(i) and if(r) of the fluxes in the r-, i-, and f-line (see, e.g., Gabriel & Jordan 1969; Porquet & Dubau 2000). In this observation, the dipole-allowed resonance transitions are seen as absorption lines, as an absorbing plasma is detected in front of the X-ray source. For the same reason, we cannot use the Fe L-shell density diagnostics (Mauche et al. 2005) as, e.g., the Fe xxii emission lines at 11.77 Å and 11.92 Å used by Mauche et al. (2003) are both seen in absorption. But we can still use the detected He-i and -f emission lines to estimate the density via the -ratio, noting the caveat that the densities are systematically overestimated in the presence of an external UV radiation field, as photoexcitation of the transition depopulates the upper level of the f-line in favor of the i-line and leads to a lower -ratio (see, e.g., Mewe & Schrijver 1978; Kahn et al. 2001; Wojdowski et al. 2008).

The i- and f-lines of the Mg xi triplet are seen as two distinct components each – one with almost no shift, which is consistent with the r-absorption line, and the other one at a redshift of 400–1000 km s (see Figure 12 and Table 8). Given these two emission components and their Doppler shifts, one could be tempted to identify the absorption feature at 9.19 Å with a second redshifted Mg xi r line, but our model for the complete absorption line series (Section 3.5) predicts that the blueshifted transitions from the ground states of Fe xxi and Fe xx, as well as the Ne x  transition, account for most of the absorption seen at 9.19 Å. Table 9 shows the -ratios obtained for the two pairs of lines as well as the corresponding densities according to the calculations of Porquet & Dubau (2000, Fig. 8e), neglecting the influence of the UV radiation of HDE 226868 on the -ratio. The unshifted lines would then be caused by a plasma with an electron density cm; the redshifted pair of lines seems to stem from another plasma component with . A more detailed discussion of these densities is presented in Section 4.1.

The S/N of the spectrum above 20 Å is not high enough to describe the O vii triplet. The Ne ix triplet blends with several Fe xix lines (Figure 11). Na x i- and f-lines are likely to be present with several components, but those cannot be distinguished clearly. Similar as for Mg, there are also two i-lines of Al xii at shifts of  km s and  km s, respectively, but no f-line is detected due to a blend with the strong Mg xi He  absorption line and especially an Fe xxii 1s2s2p(2s5p) absorption line at 7.87 Å. Similarly, the Si xiii i-line is not detected as it overlaps with absorption features probably due to nearly neutral Si K-edge structures. (Furthermore, the flux of the Si xiii f-line might be underestimated as it blends with the Mg xii Ly  line.) The i- and f-lines of He-like sulfur are detected with S xv, but S xv has not been modeled by Porquet & Dubau (2000). Below 4 Å, the S/N below is again not high enough to resolve further triplets from heavier elements such as argon, calcium, or iron.

## 4. Discussion And Conclusions

In the following, we discuss our results and derive constraints on the stellar wind in the accretion region.

### 4.1. Velocity and Density of the Stellar Wind

While a spherically symmetric model for the stellar wind in the HDE 226868/Cyg X-1 system can be excluded by observations (see, e.g., Gies & Bolton 1986b; Gies et al. 2003; Miller et al. 2005; Gies et al. 2008), a symmetric velocity law

 v(r)=v∞⋅f(r/R⋆) (12)

is usually assumed to obtain a first estimate of the particle density in the wind. The fraction of the terminal velocity is often parameterized by (Lamers & Leitherer 1993, Equation 3)

 f(x)=f0+(1−f0)⋅(1−1/x)β(for x≥1) (13)

with