Si K EDGE STRUCTURE AND VARIABILITY IN GALACTIC X-RAY BINARIES

Table 1 shows that about 40% of the observations were taken in timed event (TE) mode. Some of these data were taken in the early phases of the mission where the effects of pileup in the HETG has not yet fully been recognized and mitigated. Specifically, in observations IDs > 1000, photon pileup in grating spectra is significant, and even though there are procedures to reconstruct the data, these results have high systematic uncertainties. We include these data in the survey but treat them with caution. Most TE-mode data were taken using tight subarrays with row numbers between 300 and 420 and, consequently, much lower frame times. The bulk of the pileup events comes from the MEG +1st order where the Si K edge resides on a back-illuminated CCD. These devices have significantly higher effective areas between 1 and 3 keV than front-illuminated devices, and, in TE mode, we exclude some of these data (see Figure 1). We can, in extreme cases, eliminate significant sources of pileup by only using HEG +/−1st orders. The optical depths in the TE-mode sample are then affected up to 10% by pileup at the Si K edge in the worst cases.

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In most cases, however, pileup affects the edge by much less than 10%. We tested this on the example of GX 13+1 using the gpile2 function in ISIS, which allows a simple pileup reconstruction of HETG continuum spectra. Even though, here, we find pileup of up to 20% in the hard parts of the spectra <4 Å, the value around Si K was of the order of 8%. The continua in galactic low-mass x-ray binary spectra increase with energy, in part, because of absorption due to high column densities but also intrinsically. Thus, even though the HETG effective area is high around Si, the bulk of the photon pileup affects the hard part of the spectra. Furthermore, an edge optical depth is only affected by the pileup difference between the top and the bottom edge flux. In GX 13+1, the difference of the effective pileup at the top and bottom of the Si K edge is less than 5%. The average effect in all sources is 5%, and we correct optical depths upwards by this amount as well as add this amount to the uncertainties in optical depth and equivalent width.

The remainder of the data were taken in continuous clocking mode (CC-mode) with a fast read time (note: the frame times in Table 1 are approximate and for reference only). Here, the spectra are devoid of any pileup, and, ideally, the edge structure and optical depth are fully preserved. However, absorbed CC-mode spectra are affected by contributions from dispersions from all incident photons. In most cases, this at least includes the central source but also a substantial scattering halo. In CC-mode, these contributions collapse into a one-dimensional image, and the HETG extraction then contains the source spectrum as well as dispersed photons from the zero-order scattering halo, which get added to the dispersed first order spectra and, ultimately, will alter the spectral shape of these spectra. In addition, while in TE- and CC-mode, any contributions including the ones from higher orders are effectively filtered out by the pulse height channels in every CCD pixel; this filter is not fully effective in CC-mode. For example, the HEG first orders are confused with the MEG second orders. In the sources of this sample, the scattering halo is prominent because of the high absorption columns involved. While the edge structure remains preserved, optical depth values are affected. From comparisons with data taken in TE mode, we estimate that this effect adds about 20% systematic uncertainty to the optical depth on average.

FI devices also have an intrinsic Si K edge from the SiO₂ gate structural layer located at the atomic Si K edge location. A high resolution correction is applied in TE-mode data to account for this contribution. However, since the optical depths appear slightly reduced in CC-mode due to the effects described above, this correction cannot be properly applied, and we cannot use FI data. In BI devices there is no significant instrumental contribution to the Si K edge (see Figure 1), and in CC-mode we, therefore, exclusively use the MEG +1st order located on the S3 device. We then correct optical depths by 20% as well as add this amount to the uncertainties in optical depth and equivalent width.

The spectra were all fitted with a two-component spectral model consisting of a disk blackbody in the soft end and a power law in the hard end of the spectral bandpass plus absorbing column density for which we used the TBnew function in XSPECv12. For this continuum fit, we apply the ISM abundances from Wilms et al. (2000). The bandpass is limited at the soft end by the high column density to about 9 Å (1.4 keV) and at the high end to 5.2 Å (2.6 keV) in CC-mode spectra, leaving about 180 independent resolution bins for the spectral fitting in MEG spectra and 340 bins in HEG spectra. The spectra are well-fitted by this model, with reduced χ² values below 1.8 in the worst case. Note that in this analysis, we do not require a physical interpretation of the spectral continuum but want a good representation for flux and broadband column densities. The resulting hydrogen equivalent column densities are listed in Table 1. We will use this column as the x-scale in some of the plots. All sources are bright, with first order count rates as low as 1.4 cts s⁻¹ and as high as 77 cts s⁻¹, which translates to a flux range 1 × 10⁻⁹ to 3 × 10⁻⁸ erg s⁻¹ (0.04–1.1 Crab) in the range 2–10 keV. The column densities in the data vary from 1.23 ± 0.13 × 10²² cm⁻² in obsid 17485 for Ser X-1 and 6.84 ± 0.92 × 10²² cm⁻² in obsid 6631 for GX 340+0. The columns have low statistical yet substantial systematic errors of 10% that are added due to the limited bandpass. Most values obtained are consistent within these uncertainties for columns obtained in previous studies.

The variety of data modes and their systematic uncertainties do not allow for the direct fit of models to these data to determine sensible physical information. However, the data are good enough to deduce common trends with respect to existing models. First, we take advantage of the superbly calibrated energy (wavelength) scale of the Chandra HETG data. The scale calibration is entirely independent of the data modes and has low systematical uncertainties for all survey data. In this respect, we will determine most accurate energy (wavelength) locations of Si K edge features with mostly statistical variances of the order of about 1 eV or 4 mÅ.

Second, the optical depth of features in the Si K edge is a directly measurable quantity that is fairly independent of the detailed shape of the edge but still subject to systematical uncertainties that come with the use of various data modes. However, in the case of the optical depths, we can account for most of them. In this paper, we, therefore, survey the data in terms of how optical depths of Si K absorption features distribute among X-ray sources in the Galactic bulge and how these properties compare to predictions from existing models of atomic and silicate absorption models.

In order to explore a first cut of the structure of the Si K edge, we employ the standard edge function implemented in XSPECv12. The K edge structure can be decomposed into various elements. Standard edge parameters are the edge location (λ_SiK [Å], E_SiK [keV]) and optical depth τ gives it a step-like shape. The function, in detail, is

$$\begin{eqnarray}F(E) & = & 1\quad E\lt {E}_{\mathrm{SiK}},\quad F(\lambda )=1\quad \lambda \gt {\lambda }_{\mathrm{SiK}}\\ F(E) & = & \exp (-\tau {(E/{E}_{\mathrm{SiK}})}^{-3})\quad E\gt {E}_{\mathrm{SiK}}\\ F(\lambda ) & = & \exp (-\tau {({\lambda }_{\mathrm{SiK}}/\lambda )}^{-3})\quad \lambda \lt {\lambda }_{\mathrm{SiK}}\end{eqnarray} \tag{ 1 }$$

with an exponential edge recovery at the high energy side. The edges in the survey are also accompanied by structure, and, in all cases, they are represented as Gaussian-shaped absorption features. Figure 2 shows edge structure examples in four different sources plotted on an  Å (top) and keV (bottom) scale. The following subsections describe these structures in detail for all survey sources.

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Most previous efforts to describe neutral and near-neutral absorption edges in the X-ray band relied entirely on atomic absorption properties at or in the vicinity of the edge. In the case of silicon, this approach is incomplete since it is now assumed that at least a significant fraction of Si is bound in molecular form and conglomerated into dust grains. In that case, X-rays in the line-of-sight are affected by scattering as well as absorption, both contributing to affecting optical depth. The sum of the absorption and scattering optical depth is called extinction, and it affects radiation throughout the entire electromagnetic spectrum. Studies by Weingartner & Draine (2001), Draine (2003), and, most recently, Hoffman & Draine (2016) and Corrales et al. (2016), laid out some of the ground work on how to treat the Si K edge band with respect to both scattering and absorption.

Figure 3 shows the optical depth from the Draine (2003) model per unit column for the Si K edge for scattering, absorption, and total extinction (see, also, Corrales et al. 2016). Using the dust scattering codes of Corrales & Paerels (2015), the total Si K edge extinction cross section shown in Figure 3 (top) was calculated from a power law distribution (MRN) of dust grain sizes (see Mathis 1998), dn/da ∝ a^−3.5 where a is the radius for spherical dust grains. The minimum and maximum cut-offs to the grain size distribution were 0.005 and 0.25 μm, respectively. To calculate the Mie scattering cross section, we use the optical constants derived by (Draine 2003), which rely on laboratory Si K edge absorption measurements of silicate materials (Li et al. 1995), in this case, specifically modeling properties of olivines, i.e., Mg₂SiO₄. Figure 3 (middle) shows the same but for 0.3 μm grain sizes only. To arrive at the total opacity of the Si K edge, Figure 3 assumes that all neutral Si is locked up in dust and that all of the interstellar dust is in amorphous silicate (olivine) form. These calculations were also done using solar abundances (Asplund et al. 2009), and we use a renormalization factor (0.59 for olivine) to convert to ISM abundances (Wilms et al. 2000) used in the data analysis.

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The fit with the standard edge function determines the optical depth of the Si K edges in all survey observations. This optical depth ignores additional edge structure and treats the Si K edge as the simple step function determined by the continuum below and above the edge location (in keV units). We refer to these depths as case A. Another method used to determine the optical depth is to refer to the flux values directly below and above the edge location (in keV units), which accounts for the substructure—in this case the near edge absorption (see Section 4.3)—of the edge. Here, the optical depth is calculated by

$$\begin{eqnarray}&&\tau =\mathrm{ln}\left(\displaystyle \frac{{f}_{a}}{{f}_{b}}\right),\end{eqnarray} \tag{ 2 }$$

where f_b is the flux below and f_a is the flux above the edge location where it is lowest (with respect to energy scale). We refer to these depths as case B.

We fitted all Si K edge data with the standard edge model described in Equation (1). The unfilled circles in Figure 4 show the measured Si K edge energies E_SiK for all survey sources as a function of source flux. The measured edge energies show little variations; the smallest value we find is at 1.840 keV, and the largest is at 1.848 keV. Both of these values come from edges with lower statistics. Edge values cluster tightly around an average value of E_SiK = 1.844 ± 0.001 keV (λ_SiK = 6.724 ± 0.004 Å). Many of these edges have additional structure and the edge fit here does not take into account any contribution from the near edge absorption feature (Section 4.3), which adds a systematic uncertainty of another 0.75 eV (0.003 Å). Variations within single sources are very small; the largest deviations are, again, associated with lower statistics. We do not observe any dependence of the edge location with source flux, nor any correlations with other source or edge parameters. The expected atomic edge location is 1.839 keV (Bearden & Burr 1967), and the measured values are larger by 5 eV, which is an order of magnitude larger than the uncertainty of the HETG energy scale.

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The hydrogen equivalent column density N_H for a specific element z relates to the optical depths τ_z via the absorption cross sections σ_z as

$$\begin{eqnarray}&&{\tau }_{z}={N}_{{\rm{H}}}\times {A}_{z}\times {a}_{z}\times {\sigma }_{z},\end{eqnarray} \tag{ 3 }$$

where A_z is the abundance from a specified distribution and a_z is an over-abundance factor. Here, we generally refer to ISM abundances from Wilms et al. (2000). The atomic absorption cross section σ_z in that study has a value of 1.58 × 10⁻¹⁹ cm² from Verner & Yakovlev (1995).

Case A depths (see definition in Figure 3) show that the measured optical depths in most sources are significantly higher than expected from the ISM abundance and the atomic Si cross section (blue line; on average, about a factor 2). For all sources, we obtain a_z values of ∼2 for Si abundance factors when we fit the edges with the TBnew function and a free Si abundance parameter. Below, we will show that much of this apparent overabundance is removed when we use better Si cross sections. The scatter of the data within each of the sources (i.e., same symbols) is primarily due to the different data modes. Case B depths (see Figure 3) of all sources are much larger by factors of 1.6 (GX 349+2) up to a factor of 5 (GX 13+1) (Figure 5). The plot on the left shows the case A optical depths versus the fitted broadband column densities. Even though there is some scatter in the data, the optical depths show a good correlation with overall column. The plot on the right shows the case A optical depths versus the case B optical depths. The scatter of case B optical depths is somewhat larger. This is likely due to systematic variations from the different data modes (see Section 2.1) as well as variability in the near edge absorption features (see below).

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These depth excesses cannot be attributed to any of our measuring deficiencies as either pileup in TE mode as well as imaging distortions in CC-mode would reduce our edge optical depth determinations. Note, 4U 1624–49 is exceptional in that the depth is higher by about a factor of 5 for case A, but, here, the case for substantial intrinsic absorption is known (Xiang et al. 2009). It is also interesting to note that the data do not show any near edge absorption (case A = case B).

The Si K edge structures in Figure 2 show significant absorption close to the bottom of the edge function. We modeled the properties of this absorption by fitting a broadened Gaussian function to the data. The filled squares in Figure 4 show the centroids of the absorption line fits. Their values lie between 1.844 and 1.852 keV with the bulk fit at 1.849 + 0.002 KeV (6.706 ± 0.006 Å). In some cases, this absorption feature has very low contrast with respect to the edge function, and the centroid fit overlaps with the actual edge location. In the MEG, where we have most of our data, we observe this as a smeared but steep and unresolved edge drop. The average offset of the absorption centroid with respect to the edge location is about 5 eV.

Figure 6 (left) shows the measured near edge absorption equivalent widths with respect to column density for all survey observations. The equivalent widths cover a range of values between 0.6 and 8 mA. The horizontal hatch-dot line at 0.6 mA marks the non-detection limit for most observations, and any value below that line is an upper limit. The red line marks a regression to the lowest values in all sources. It is very close to the equivalent widths would we expect from the models in Figure 3. There is a correlation of equivalent widths with column density in that the equivalent widths become larger with increasing column density. This is not surprising, as this reflects the general behavior of absorbing power on the curve of growth. However, there are many widths that are above the expectation from the model, and there is a significant amount of scatter.

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We also modeled the far edge absorption feature using a Gaussian function. The centroids are plotted in Figure 4 as unfilled squares. The values center tightly around 1.865+/−0.001 keV (6.648 ± 0.005 Å). The straight line fit is the location of the rest wavelength of the resonance line of He-like Si xiii as listed in APED⁴ and XSTAR.⁵ The actual fit to the values is almost identical to this line, and we identify this feature with Si xiii.

The measured equivalent widths (see Figure 6, right) range between 0.6 and 8 eV and are similar to the values observed in the near edge absorption feature. In the case of the far edge feature, however, many values are not significantly detected, and measurements scatter near or below the detection threshold. The correlation of equivalent width with column density is much less pronounced compared with the near absorption case, which is expected, as most of that feature comes from plasma material close to the sources.

We noticed that, even though in many sources the general appearance of the Si K edge seemed quite similar, there were also some major differences. Most apparent was the difference between 4U 1624–49, which hardly shows any structure, i.e., the case A optical depth is equal to the case B optical depth, and GX 5–1, which perhaps exhibits the most prominent pattern, i.e., the case A optical depth is significantly smaller than the case B optical depth, even though both sources have large columns.

When we compare different observations of the same source, we find that both near and far edge absorption appear variable. This is the case in at least half of the sources in the sample. This variability cannot be explained by differences in observing and detector modes; in many cases, the variability in the pattern is present while a source is observed at similar source flux and in the same detector mode. We searched for correlations with observed source flux and found none. More important here is the slope of the continuum well above the Fe K edge, because these photons are mostly responsible for Si K shell ionization. However, we do not have statistical significance in the HETG data in this specific bandpass. Unfortunately, we also cannot use the zeroth order spectrum, because it is so heavily piled up, and, therefore, we cannot investigate this issue further with our available data. In the following, we focus on some prominent examples.

GX 5–1 is the brightest source in the sample, with flux values exceeding 1 Crab. There are six observations in the Chandra archive. The first observation (Obsid 715) appears to fit quite well to the established silicate dust models, as was shown by Ueda et al. (2005). Other observations of this source are different though. The panels on the left in Figure 7 show, probably, the best example of a multi-peaked K edge structure as observed in Obsid 5888. The fit shows the edge and the far edge absorption feature leaving the near edge absorption feature as a residual. The right panel shows a sum of observations a few years later, i.e., Obsids 10691-4. While the former features a strong far edge absorption feature, the latter, in contrast, show very weak far edge absorption. Here, interestingly, we see significant Si xiv absorption. This indicates a shift in the ionization parameter of atomic Si. In Obsid 5888, we measure an equivalent width of 5.6 mÅ for the Si xiii resonance line, while in Obsids 10691-4, the average equivalent width is very close to the detection limit of 0.6 mÅ. The near edge absorption, on the other hand, is significant in all observations, but the equivalent widths vary from 3.8 to 7.6 mÅ with a 90% uncertainty of about 0.5 mÅ.

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Perhaps the most intriguing source is GX 13+1, where we have six very similar observation segments distributed over weeks and years. Figure 8 shows these observations in sequence. Obsid 2708 was the one used by Ueda et al. (2005) in their Si K edge analysis. Readily detected is strong H-like Si xiv absorption stemming from an accretion disk wind reported by Ueda et al. (2004) also using Obsid 2708. However, we find that the Si K edge structure is highly variable in the observations of GX 13+1, and while we can apply the dust model from Ueda et al. (2005) in Obsid 2708 with some minor residuals, we cannot reproduce such a fit in the other observations. We now identify the far edge absorption feature with He-like Si xiii resonance absorption and observe variations in equivalent widths from <0.6 mÅ to about 4 mÅ. The 90% uncertainties are of the order of 0.7 mÅ. Near edge absorption is present in all observations; however, again, with significant variations in equivalent widths. Equivalent widths vary from 1.4 to 7.4 mÅ.

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For the two sources, GX 5–1 and GX 13+1, we also fitted a warm absorber model to the Si K edge data, where we fixed the TBnew(1).nh parameter to the values in Table 1. For the warm absorber model, we use the XSTAR function warmabs in XSPEC. We fixed the parameters of the near edge absorption function to the near edge locations and to the observed case B optical depths with a width equivalent to the HEG resolution. Such a function mimics a basic Si K edge structure. The ionization parameter log ξ was constrained to values between 1.6 and 2.0. Here, the Si xiii line absorption is strong and Si xiv is still weak. In GX 13+1, we added a warm absorber with log ξ = 3 in order to account for the apparent Si xiv absorption feature from a known disk wind Ueda et al. (2004). We tested the warm absorber model for three specific cases, GX 5–1 (Obsid 5888), GX 13+1 (Obsids 2708, 11814), and GX 13+1 (Obsids 11815, 11816). In the last, Si xiii is hardly detected, and, here, we see the least ionized case and a more accurate silicate edge structure. The warm absorber needs high turbulent velocities (>700 km s⁻¹) in order to fit the full Si xiii feature width but also to smooth out small absorption features that are nested in the continuum noise. This fact makes the fit very difficult, because this creates a lot of shallow minima in the fit parameter space and allows for multiple solutions. In that respect, such a simple warmabs fit is not unique. This effect was minimized by constraining the ionization parameter (log ξ) to 1.6 on the low side and 2.0 on the high side for finding the best fit. To compute 90% confidence limits, we then released the constraint and got values for GX 5–1 of 1.8 ± 0.3 and GX 13+1 of 1.9 ± 0.3. If we would not constrain the fit first, lower values down to 1.1 were found as well. In general, these fits are able to provide for the major features and their variability near the Si K edge.

Variations of EW span similar ranges among different sources and observations. The source 4U 1624–49 is different in a sense that it is the only one where we do not observe significant near edge absorption but high far edge absorption, which stems from an identified warm absorber in the accretion disk (Xiang et al. 2009).

Ser X-1 is the source with the lowest overall column (1.2 × 10²² cm⁻²). An early Chandra observation was pileup-dominated and mostly useless (OBSID 700), but we carried out two observations in TE mode with a very narrow subarray (134 rows, OBSIDs 17485, 17600), reducing pileup to less than 3% at the Si K edge. Here, we do not observe any edge structure in the MEG spectrum and only a very weak and unresolved near edge feature in the HEG.

• 1.  
  The Si K edge, as measured using Chandra, has significant substructure and consists of an edge at 1.844 ± 0.001 keV, additional near edge absorption at 1.850 ± 0.002 keV, and far edge absorption at 1.865 ± 0.001 keV.
• 2.  
  The Si K edge structure cannot be fit by a common silicon dust model as was done in a more limited previous study by Ueda et al. (2005).
• 3.  
  The Si K edge structure in X-ray binaries appears highly variable in timescales of days to weeks and should be explained using local ionization effects.
• 4.  
  The far edge absorption feature is identified as Si xiii resonance absorption in the close vicinity of the X-ray binaries’ accretion disk.
• 5.  
  Variations in far edge absorption features include the appearance of Si xivresonance absorption in some cases and are an expression of changing ionization parameters in circum-binary material.
• 6.  
  The bulk of the Si K edge systematically appears at a value where silicate absorption is expected; however, the associated near edge absorption also appears variable, possibly indicating local ionization effects in silicon compounds.
• 7.  
  Comparisons with extinction models show that the Si K edge optical depth is determined by contributions from absorption and significant amounts of scattering.
• 8.  
  A preliminary comparison of Si K edge optical depths obtained from models using different grain sizes suggests that larger grain sizes are favored.
• 9.  
  Data from highly resolved edges with good statistics indicate the presence of an additional edge at 1.840 keV, with about 10% of the optical depth likely coming from atomic silicon.
• 10.  
  The Si K edge in X-rays then has several contributions to consider: absorption from atomic silicon and from silicates attenuated by considerable contributions of scattering optical depths and variable ionized absorption features.

Future studies should focus on the variability and multiplicity aspect of the Si K edge structure and substructure as well as scattering optical depths. We are in the process of gathering more data that is less affected by instrumental effects, in order to further study the possibility of multiple edge components. Future observations made during the upcoming X-ray spectroscopy mission Astro-Hwill become instrumental and most fruitful for these studies.