Canonical X-Ray Fluorescence Line Intensities as Column Density Indicators
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Canonical X-Ray Fluorescence Line Intensities as Column Density Indicators
Roi Rahin and Ehud Behar Physics Department, Technion, Haifa 32000, Israel (Received; Revised; Accepted)
Submitted to ApJABSTRACTX-ray line fluorescence is ubiquitous around powerful accretion sources, namely active galactic nucleiand X-ray binaries. The brightest and best studied line is the Fe K α line at λ = 1 . α fluorescence lines from elements between Mg and Ni. Despite the variety of sources and physicalconditions, we identify a common trend that dictates the K α line intensity ratios between elements.For the most part, the line intensities are well described by a simple, plane-parallel approxima-tion of a near-neutral, solar-abundance, high column density ( N H > cm − ) medium. Thisapproximation gives canonical photon-intensity line ratios for the K α fluorescence of all elements,e.g., 0.104: 0.069: 1.0: 0.043 for Si: S: Fe: Ni, respectively. Deviations from these ratios are shownto be primarily due to excess column density along the line of sight beyond the Galactic column.Therefore, measured fluorescence line ratios provide an independent estimate of N H and insightinto the environment of accretion sources. Residual discrepancies with the canonical ratios couldbe due to a variety of effects such as a fluorescing medium with N H < cm − , a non-neutralmedium, variations in the illuminating spectrum, non-solar abundances, or an irregular source geom-etry. However, evidently and perhaps surprisingly, these are uncommon, and their effect remains minor. INTRODUCTIONX-ray fluorescence is a natural consequence of pow-erful X-ray sources illuminating ambient, cold material.Inner-shell ionization or excitation of neutral or near-neutral ions from the K-shell may be followed by de-cays filling the K-shell vacancy, and resulting in K α andK β emission lines. Near neutral ions are loosely definedhere as all ions whose K α line can not be distinguishedfrom that of the neutral atom with contemporary X-ray spectrometers, i.e. ∆ λ (cid:46)
20 m˚A. K-shell lines fromnear-neutral species are generally referred to as X-rayfluorescence lines.Fluxes of K-shell fluorescence lines from various el-ements have been measured for a few bright sources(e.g., Sako et al. 1999), but no simple explanation existsfor their relative intensities. These intensities may de-pend on several parameters, such as the elemental abun-dances, and the fluorescence yields. The fluorescence
Corresponding author: Roi [email protected] yield is the probability that an inner-shell excited ionwill decay radiatively (i.e. fluorescence), and not auto-ionize (Auger decay), both decays being spontaneous.For low- Z elements ( Z < ∝ Z in the hydrogenic approximation),while auto-ionization rates are essentially independentof it (Bambynek et al. 1972). Consequently, the fluores-cence yields increase slowly with the atomic number, upto ∼
35% for Fe, which produces the most prominentfluorescence K α line.To complicate things, the intensities of the various flu-orescence lines depend not only on the atomic proper-ties, but also on those of the fluorescing medium. The X-ray intensity reaching and exciting the atoms depends onthe radiative transfer of the external continuum sourceinto this medium, which depend on the internal ioniza-tion and temperature structure of the medium (Dopitaet al. 2002; Stern et al. 2014, and references therein).The near-neutral species emitting fluorescence lines cansurvive the high X-ray field only if the ionization param- a r X i v : . [ a s t r o - ph . H E ] S e p eter ( L/nr ) is low. Here L is the source luminosity, n isthe number density of the fluorescing medium and r is itsdistance from the source. This requirement suggests flu-orescence lines originate in the denser (possibly clumpy)parts of the medium (Sako et al. 1999; Sambruna et al.2000; Sako et al. 2000; Yaqoob 2012; Kallman et al. 2013;Ar´evalo et al. 2014; Xu et al. 2015).The physical scale of fluorescing gas remains uncer-tain, even in similar-type sources, such as Seyfert 2s.Sako et al. (2000) observed fluorescence from gas overhundreds of pcs in Mrk 3. Sambruna et al. (2000) foundthe fluorescing medium in the Circinus galaxy to be con-centrated within 15 pc of the nucleus, although Marin-ucci et al. (2013) and Ar´evalo et al. (2014) later foundevidence for significant flourescense by cold gas from anextended ionization cone out to ∼
100 pc. In NGC 4151Ogle et al. (2000) found K α emission extended out to ∼
200 pc, while Miller et al. (2018) place the emissionwell below 1pc. In X-ray binaries, the geometry andmorphology of the fluorescing source can be studied fromthe variability due to the binary orbit (e.g., Watanabeet al. 2006).Finally, the observed fluorescence line intensity de-pends also on the probability of the line photons escap-ing the medium and into our line of sight. For example,resonant absorption of lines by the same atomic speciesthat emitted them can be followed by auto-ionization,which essentially eliminates the fluorescence-line pho-ton. This process has been termed resonant Auger de-struction, and depends on the details of the atomic stateof the emitting and absorbing atoms (Ross et al. 1996;Liedahl 2005). The effect of radiative transfer on spec-tral lines is a complex problem influenced by the mediumgeometry and the illuminating spectrum and has beencomprehensively treated by several codes (George &Fabian 1991; Netzer 1996; Kallman & Bautista 2001;Ferland et al. 2017).In this work, we aim to present all high S/N X-rayspectra of accreting sources, namely active galactic nu-clei (AGN) and X-ray binaries (XRB), which featurefluorescence lines from several elements. We focus onthe astrophysically abundant elements up to Ni. Low-Z fluorescence from elements lighter than Mg are rarelyobserved, due to their low fluorescence yield. Hence, thispaper represents a comprehensive survey of K-shell fluo-rescence from Mg - Ni. The goal of the present study isto seek common attributes of fluorescence lines, despitethe variety of physical conditions occurring around ac-cretion sources, and despite the apparent complexity ofthe atomic states and radiative transfer.For this purpose, we use the archive of the Chan-dra/HETG grating spectrometer, for its high spectral resolution and low background. These attributes in-crease the confidence in the detection of the weakestfluorescence lines. The targets and data reduction aredescribed in Sec. 2. The common themes across sourcesare presented in Sec. 3. A simple plane-parallel model isdescribed in Sec. 4, and its adequacy for explaining theobserved line intensities is presented in Sec. 5. Finallyin Sec. 6 we present our conclusions. OBSERVATIONSWe use observations of the Chandra HETG with highquality spectra, which exhibit at least four significantfluorescence lines. The objects are either Seyfert 2s orhigh-mass XRB. All data were processed by The Chan-dra Grating-Data Archive and Catalog, TGCat (Huen-emoerder et al. 2011). In the following, we briefly intro-duce each target and its relevant observations.2.1.
The Circinus Galaxy
The Circinus galaxy is a Seyfert 2 at redshift z =0 . NGC 1068
NGC 1068 is a Seyfert 2 ( z = 0 . Markarian 3
Markarian 3 is a Seyfert 2 ( z = 0 . NGC 4151
NGC 4151 is an AGN ( z = 0 . α lines vary, es-pecially Fe and Si K α (Table 9), which is most likely aresult of variable source luminosity. To improve read-ability, figures in the present paper include only a jointmeasurement of the last two observations, which havesimilar spectra. 2.5. Vela X-1
Vela X-1 is a high mass, eclipsing, X-ray binary. VelaX-1 was observed by the HETG eight times between2000 and 2017. Unlike AGN, the spectrum of X-ray bi-naries varies significantly over short time periods (e.g.,Belloni & Hasinger 1990; Kreykenbohm et al. 2008).The variation is in large part due to the orbital position(Watanabe et al. 2006). As such, each observation wasanalyzed separately. The observations used are listedin Table 6. The HETG spectrum of Vela X-1 was an-alyzed in Schulz et al. (2001); Goldstein et al. (2004);Watanabe et al. (2006).The HETG observed Vela X-1 in several phases. Ac-cording to Watanabe et al. (2006) observation 1926 wasmade at phase 0.98-0.093 and 1927 at phase 0.481-0.522.Based on these data and on the Vela X-1 period of8 . ± . GX 301-2
GX 301-2 is a non-eclipsing high mass X-ray binary.GX 301-2 was observed three times by the ChandraHETG in the years 2000 and 2002. The GX 301-2spectrum shows significant and variable column density(Mukherjee & Paul 2004; Islam & Paul 2014); however,it is hard to determine how much of it affects the fluores-cence lines. The HETG observed GX 301-2 in 3 differentphases: 0 . − . . − . . − . DATA ANALYSISWe perform the spectral analysis using Xspec version12.10.1f (Arnaud 1996). We focus only on the total fluxof the narrow fluorescence lines, which are measured byfitting a Gaussian to each line. The line widths of localSeyfert 2s in grating spectra are broadened by their an-gular extent, which impedes the extraction of kinematics and thus location of the fluorescing medium. However,our analysis is unaffected by kinematic or instrumentalbroadening. When calculating line fluxes at the sourcewe include neutral absorption representing the Galac-tic column density (Dickey & Lockman 1990; Kalberlaet al. 2005; Bekhti et al. 2016), assuming solar abun-dances (Asplund et al. 2009). The measurements aresummarized in Tables 7, 8, and 9.3.1.
Si and Mg K α The Si K α line at 7.126 ˚A blends with the Mg XIILy β line at 7.106 ˚A. To best estimate the Si K α flux,we approximate the flux of the Mg XII Ly β based on itsLy α counterpart at 8.421 ˚A. The flux of the Ly β lineis assumed to be 20% that of the Ly α line based onthe Xstar code (Kallman & Bautista 2001). We thusmeasure the flux in the Mg XII Ly α line, and subtract20% of it from the Si K α measured flux. This fractionis also supported by the analysis of Liu et al. (2016).The Mg K α line at 9 .
890 ˚A suffers from low signal. InNGC 1068 we identify another line at ∼ .
843 ˚A (restframe) with comparable flux, which we include in thetotal Mg K α flux. This may indicate fluorescence fromslightly ionized Mg in NGC 1068.3.2. Fe K β Apart from all K α lines we also measure the Fe K β fluxes. These are hampered by the diminishing effec-tive area of the HETG and the neighboring H-like andHe-like Fe lines. The Fe K β /K α photon-intensity ra-tio ranges from 0.1-0.3 with large uncertainties (Tables7 and 8). Laboratory measured ratios are 0.115-0.15and theoretically up to 0.165 for Fe IX (Palmeri et al.2003, and references therein). The present measure-ments are mostly consistent with these values, exceptfor the brightest phases of GX 301-2 and Vela X-1 whenthe ratio is higher. This could possibly be explainedwith even higher ionization.3.3. Luminosities
We calculate the luminosity of the different fluores-cence lines in various AGN and XRB by assumingisotropic emission. The results are shown in Figure 1.Although the sources vary greatly in luminosity, we notea general decreasing intensity trend with Z in the AGNand a flatter trend in the XRB. Fe K α remains thebrightest line by far in all sources. Understanding thesetrends is the goal of the present paper.3.4. Relative intensities
We aim to compare the relative strength of the flu-orescence lines of various objects. We used the Fe K α flux in each object to normalize the fluxes, as it is themost prominent fluorescence line and thus has the small-est measurement uncertainties. The relative fluxes areshown in Figure 2. In the next section, we present asimple theoretical model to explain these relative inten-sities.
12 14 16 18 20 22 24 26 28Atomic number Z10 L u m i n o s i t y [ e r g s − ] CircinusNGC 1068 MRK 3NGC 4151
12 14 16 18 20 22 24 26 28Atomic number Z10 L u m i n o s i t y [ e r g s − ] Vela X-1 pre-eclipseVela X-1 eclipseVela X-1 post-eclipseVela X-1 0.15Vela X-1 0.5 Vela X-1 0.75GX 301-2 IMGX 301-2 NAGX 301-2 PP
Figure 1.
Luminosity of K α fluorescence lines corrected forGalactic absorption. Top : AGN.
Bottom : XRB. Note thesimilar trends in AGN despite the disparity in luminosityand the phase dependence in the XRB.4.
MODEL FOR X-RAY FLUORESCENCEWhen a dense neutral medium is illuminated by anX-ray source the various elements in the medium maybe excited and produce X-ray fluorescence. The fluores-cence from each element in each layer in the medium isproportional to the intensity of radiation reaching thatlayer.The following derivation was adapted from Thomsen(2007). In a plane parallel approximation the incidentphoton-intensity I ( E, x ) at energy E and depth x intothe medium is: I ( E, x ) = I ( E, e − τ ( E,x ) (1)where τ ( E, x ) is the total optical depth a distance of x into the medium, given by: τ ( E, x ) = (cid:90) x σ ( E ) n H dx = σ ( E ) N H (2)
12 14 16 18 20 22 24 26 28Atomic number Z10 -4 -3 -2 -1 R e l a t i v e I n t e n s i t y CircinusNGC 1068MRK 3NGC 4151 GX 301-2 IMGX 301-2 NAGX 301-2 PPVela X-1 eclipse
12 14 16 18 20 22 24 26 28Atomic number Z10 -4 -3 -2 -1 R e l a t i v e I n t e n s i t y Vela X-1 pre-eclipseVela X-1 eclipseVela X-1 post-eclipse Vela X-1 0.15Vela X-1 0.5Vela X-1 0.75
Figure 2. K α fluorescence line fluxes plotted relative to theflux of the Fe line. The Fe line is by far the strongest by1 to 3 orders of magnitude depending on the source. Top :The source sample with a single Vela X-1 observation. Theintensities do not, by themselves, reveal an inherent distinc-tion between AGN and XRB.
Bottom : All Vela X-1 epochsstudied in this paper, suggesting a connection between lineratios and orbital phase. where σ ( E ) is the abundance-weighted average photo-ionization cross section per H atom, n H is the hydrogennumber density, and N H is the hydrogen column density.The K-shell ionization probability of a specific neutralelement Z by incident radiation at depth x is: dτ Z,K = σ Z,K ( E ) n Z dx = A Z σ Z,K ( E ) n H dx (3)where σ Z,K is the K-shell ionization cross section of ele-ment Z , A Z is the elemental abundance (assumed to besolar, Asplund et al. 2009), and n Z = A Z n H is the num-ber density of element Z . Thus, the intensity decrementdue to K-shell ionization by an element Z at a depth of x in the medium is given by: dIdx = (cid:90) ∞ E K,Z I ( E, e − τ ( E,x ) A Z n H σ Z,K ( E ) dE (4)where E K,Z is the energy of the K-edge.After a K-shell electron is released the ion can decaymainly through K α fluorescence, namely a 1s-2p transi-tion. The probability for K α fluorescence is a factor ofthe fluorescence yield, ω K , and the probability of a 1s-2ptransition over a 1s-3p transition. Higher order transi-tions are relevant only for heavy elements ( Z ≥ ω Kα , is given by: ω Kα = ω K I Kα I Kα + I Kβ (5)Values of ω K range from ∼ .
03 for Mg to ∼ .
42 forNi. The branching ratio for K α over K β emission variesfrom ∼ ∼ . ω K we adopt thevalues from Hubbell et al. (1994) as they are consistentwith experiments (S¸ahin et al. 2005) and more recentnumerical calculations (Palmeri et al. 2012). For thebranching ratio we adopt the values of Scofield (1972) toensure all values are taken from the same source. Othervalues (H¨olzer et al. 1997; S¸ahin et al. 2005; Palmeriet al. 2012) can change ω Kα by ∼
2% at most, which isnegligible relative to the line flux uncertainties (Tables7,8,9). As noted by Palmeri et al. (2003), the branchingratio decreases with ionization. The ionization uncer-tainty affects ω Kα more than that of the atomic data,but is still smaller than the measurement uncertainties.Finally, to reach us, the emitted fluorescence photonmust escape the medium. The resulting attenuation isgiven by the optical depth out of the medium at theenergy of the K α line, τ ( E Kα,Z , x ). The observed inten-sity of the fluorescence line from the entire medium upto x tot is: I f = ∞ (cid:90) E K,Z x tot (cid:90) I ( E, e − τ ( E,x ) − τ ( E Kα,Z ,x ) A Z n H ω Kα σ Z,K ( E ) dxdE (6)Solving the integral over x yields: I f = A Z ω Kα ∞ (cid:90) E K,Z I ( E, σ Z,K ( E ) σ ( E ) + σ ( E Kα,Z ) (1 − e − τ ( E ) − τ ( E Kα,Z ) ) dE (7)where τ ( E Kα,Z ) ≡ τ ( E Kα,Z , x tot ) is the optical depthof the medium at the K α line and τ ( E ) ≡ τ ( E, x tot ) isthe total optical depth of the medium. In this equation,the factors most dependent on element are A Z and ω Kα (see Table 1).Two approximations for Equation (7) can be used.First, we consider an optically thin medium. In this case1 − e − τ ( E ) − τ ( E Kα,Z ) ≈ τ ( E )+ τ ( E Kα,Z ). Since τ = σN H Equation (7) now scales linearly with N H : I thinf = A Z ω Kα N H (cid:90) ∞ E K,Z I ( E, σ Z,K ( E ) dE (8)We assume a power-law ionizing spectrum of the form I ( E,
0) = I ( E/E ) − Γ and a power-law dependence of Table 1.
Canonical I thickf intensities of X-ray fluorescence linesrelative to Fe K α . Element ω Kα Solar Abundance Relative Intensity
Mg 0.0291 3 . × − . . × − . . × − . . × − . . × − . . × − . . × − . . × − . . × − . × − . σ Z,K ( E ) = σ Z,K ( E K,Z )( E/E
K,Z ) − . (Yaqoob et al.2001) to get: I thinf = 1Γ + 1 . I E Γ0 A Z ω Kα N H E − Γ k,Z σ Z,K ( E k,Z ) (9)The second approximation of Equation (7) is for anoptically thick medium, i.e. both τ ( E ) → ∞ and τ ( E Kα,Z ) → ∞ : I thickf = A Z ω Kα ∞ (cid:90) E K,Z I ( EE ) − Γ σ Z,K ( E ) σ ( E ) + σ ( E Kα,Z ) dE (10)This approximation turns out to be the model of refer-ence for fluorescence lines in most astrophysical sources.The relative K α line intensities predicted by Equation(10) are listed in Table 1. The values for the abundances A Z and fluorescence yields ω Kα , which drive these in-tensities, are also given. It can be seen that the nextstrongest line after Fe K α is Si K α , which is expectedto be ∼
10% of the intensity of the Fe line.A comparison between the approximations and themodel for various column densities appear in Figure 3,as well as a comparison between different power-law pro-files. Figure 3 shows that dramatic changes in the powerlaw index are required to significantly change the line ra-tios. Note that the effect of a steep power-law is similarto that of an optically thin medium. In both cases thereis a lack of hard-photon excitations. RESULTS5.1.
Comparison to theory
The prevailing hypothesis assumes AGN to be sur-rounded by dense obscuring material. Some XRB, such
12 14 16 18 20 22 24 26 28Atomic number Z10 -4 -3 -2 -1 R e l a t i v e I n t e n s i t y I thinf N H =10 cm − N H =10 cm − I thickf N H =10 cm −
12 14 16 18 20 22 24 26 28Atomic number Z10 -4 -3 -2 -1 R e l a t i v e I n t e n s i t y Γ=1Γ=2Γ=3
Figure 3. Top : Relative flux of K α fluorescence linesoriginating from different column densities of the fluoresc-ing medium (Equation (7)). All models are plotted relativeto the Fe line of I thickf . I thinf (Equation (9)) agrees wellwith Equation (7) for N H = 10 cm − , except for Mg where τ ( E K,Mg ) (cid:28) I thickf (Equation (10)) isvalid for N H ≈ cm − for all elements, and for Mg, Si,and S already at N H ≈ cm − , since heavier elementsemit from deeper within the medium. Bottom : I thickf for different power-law indices (Equation(10)). All models are plotted relative to the Fe line of theΓ = 2 model. A steeper power-law causes less ionization ofhigh-Z elements and thus higher ratio of the low- Z ( Z < as GX 301-2, also show significant obscuration. Such anenvironment calls for the approximation of an opticallythick fluorescing medium. Therefore, we first comparethe measured fluxes with I thickf described in Equation10. Figure 4 shows a comparison between the measure-ments and theory for three values of Γ. As can be seen,the effects of the power-law slope are moderate com-pared to the spread in the data.From the graph we see that the measurements fromNGC 1068, MRK 3, and NGC 4151 are well described byEquation (10). Fluorescence lines from M51 (Xu et al.2015), though not measured with gratings, show a sim-ilar trend. The nominal ratios imply the line-of-sighttowards the fluorescing medium, as opposed to that to-wards the Seyfert 2 nucleus, is unobstructed. Vela X-1also shows a decent agreement with I thickf , which implies that the observed fluxes may be explained by reflectionfrom a high N H wind. This is in contrast to Sako et al.(1999) who assumed reflection from a low N H stellarwind, which caused the deduced N H values to increasewith Z .Unlike the other sources, Circinus and GX 301-2 showa systematic discrepancy of all low-Z elements with the-oretical values of I thickf . The following sections will at-tempt to provide an explanation to this discrepancy.
12 14 16 18 20 22 24 26 28Atomic number Z10 -4 -3 -2 -1 R e l a t i v e I n t e n s i t y CircinusNGC 1068MRK 3NGC 4151 GX 301-2 IMGX 301-2 NAGX 301-2 PPVela X-1 eclipse
12 14 16 18 20 22 24 26 28Atomic number Z10 -4 -3 -2 -1 R e l a t i v e I n t e n s i t y Vela X-1 pre-eclipseVela X-1 eclipseVela X-1 post-eclipse Vela X-1 0.15Vela X-1 0.5Vela X-1 0.75
Figure 4.
Relative flux of K α fluorescence lines (datapoints) compared to I thickf (Equation (10)) with variouspower-law slopes: Γ = 2 .
3, Γ = 2 and Γ = 1 . Top : The present sourcesample with a single Vela X-1 epoch. The relative intensitiesof NGC 1068, Mrk 3, NGC 4151, and Vela X-1 eclipse followthe I thickf ratios, while those of GX 301-2 and Circinus showsignificant deficiency in the low- Z lines. Bottom : All VelaX-1 epochs studied in this paper. Notice the deficiency inMg, Si, and S line fluxes in non-eclipse observations relativeto I thickf . Resonant Auger Destruction
Sako et al. (1999) proposed that Auger destructionmay have a significant effect on fluorescence lines in VelaX-1 (see Section 1). A later theoretical analysis doneby Liedahl (2005) showed the process to be complexand highly dependent on the ionization and excitationstate of each element. Indeed, K α lines of L-shell Si ina laboratory photo-ionized plasma experiment showedno evidence of resonant Auger destruction (Loisel et al.2017). Despite the complexity, several restrictions areimmediately evident. First, K α Auger destruction can-not occur in a neutral medium as it requires an L-shellvacancy. Hence, higher Z elements require higher ioniza-tion for K α photo-excitation to occur. K β , in contrast,can be quenched by Auger destruction in lower chargestates. Additionally, the energy difference between theK α energy of different L-shell Si ions is (cid:38)
10 eV. Thus,the velocity shear required to kinematically mix neigh-boring ions needs to be ∼ − , which is notobserved.In a partially ionized medium, the ions may act asresonant absorbers for the emitted K α lines. Since ω Kα (cid:28)
1, we can approximate the resulting Auger de-struction as restricting our line of sight into the mediumup to a photo-excitation optical depth of unity, τ P E = 1.The absorption cross section at the center of a resonantline under assumption of a Gaussian line profile is: σ P E = πe fm e c √ π ∆ ν (11)where e is the electron charge, m e is the mass of the elec-tron, c is the speed of light, f is the oscillator strengthand ∆ ν is the Doppler width (standard deviation). Weassume ∆ ν/ν = 0.001, which is just under the HETGresolving power.The column density of an element Z for an opticaldepth τ P E = N Z σ P E = 1 is: N Z = m e c √ π ∆ νπe f (12)Since N Z = A Z N H , the corresponding N H for abun-dant elements is smaller than for rare elements. Con-sequently, for abundant elements N H < cm − andthus τ ( E ) (cid:28) τ P E = 1. We can therefore use Equation(9) to get I thinf in the case of dominant Auger destruc-tion: I thinf = 1Γ + 1 . I E Γ0 ω Kα m e c √ π ∆ νπe f E − Γ K,Z σ Z,K ( E K,Z )(13)Equation (13) is independent of A Z , so all abundantelements will have similar I thinf . For the rarer elements τ ( E ) (cid:28) τ P E = 1 no longer holds. Thus, we must use theaccurate expression (Equation 7 with the corresponding N H ).Another possible approximation is for Auger destruc-tion in an optically thick medium. We assume thecross section for resonant absorption to be σ eff,Z = (1 − ω Kα,Z ) σ P EZ , effectively assuming the scattering isdestructive with probability (1 − ω Kα,Z ). This approx-imation effectively adds A Z σ eff,Z to the denominatorof Eq (10), which yields similar results to Equation (7)with the N H corresponding to Equation (12).Both approximations are shown in Figure 5, neither ofwhich produces a good agreement with any observation.Selective Auger destruction could explain the low-Z rel-ative intensities of Circinus, if somehow Fe is unaffected.The K β /K α nominal ratios presented in Sec. 3.2 (e.g.,0.14 for Circinus) further argue against a significant roleof Auger destruction, which is discussed in Section 6.
12 14 16 18 20 22 24 26 28Atomic number Z10 -4 -3 -2 -1 R e l a t i v e I n t e n s i t y CircinusNGC 1068MRK 3NGC 4151 GX 301-2 IMGX 301-2 NAGX 301-2 PPVela X-1 eclipse
12 14 16 18 20 22 24 26 28Atomic number Z10 -4 -3 -2 -1 R e l a t i v e I n t e n s i t y Vela X-1 pre-eclipseVela X-1 eclipseVela X-1 post-eclipse Vela X-1 0.15Vela X-1 0.5Vela X-1 0.75
Figure 5.
Relative flux of K α fluorescence lines comparedto theoretical ratios predicted by Auger destruction mod-els. The blue line describes I thinf where the optical depth islimited by photo-excitation (Equation (13)). The black linedescribes I thickf , but with Auger resonant scattering factoredin. All models are normalized relative to the theoretical Feline flux of I thickf (Equation (10)). Excess Line of Sight Column Density
We propose a simple explanation to the relativelyweak low- Z lines observed in several of the present mea-surements. The deficiency of the low-Z relative intensi-ties with respect to I thickf (Figure 4) decreases with Z.Therefore, excess line of sight column density beyondthe Galactic column could explain the anomalous ra-tios. If correct, a single column density value N ex H foreach object would need to explain the quenching of thefluorescence lines of all low-Z elements. We can then usethe measured fluxes to estimate N ex H self-consistently foreach object. The observed intensity ratio with an addi-tional column density N ex H would be: I obsf,Z I obsf,F e = I thickf,Z e − σ ( E K,Z ) N ex H I thickf,F e e − σ ( E K,Fe ) N ex H (14)Thus we can extract N ex H for each element: N ex H = 1 σ ( E K,F e ) − σ ( E K,Z ) ln (cid:32) I obsf,Z I obsf,F e I thickf,F e I thickf,Z (cid:33) (15) N ex H as derived by Si K α is the most reliable estimate,as it is the best measured line except for Fe K α , andtheir cross section difference is the second highest. ForSi Equation (15) gives: N ex H (Si) = 2 . × ln (cid:32) . I obsf,F e I obsf,Si (cid:33) (16)In extra-galactic sources excess column density canbe associated with dust extinction and reddening. InNGC 1068 the above line ratios show only marginal ev-idence for N ex H , which is consistent with the low red-dening towards the narrow line region of NGC 1068( A V < .
15, Crenshaw & Kraemer 2000). In Mrk 3only Mg and Si K α require marginal excess column den-sity of N ex H (Mg) = 1 . +0 . − . × cm − and N ex H (Si) =0 . ± . × cm − respectively, while other elementsprovide only an upper limit of N ex H < × cm − .This value is consistent with the reddening based esti-mate of Collins et al. (2005) of N H ∼ cm − .In the NGC 4151 combined 2014 observations the K α intensity ratios of Mg, Si and S to Fe predict a columndensity of N ex H ∼ × cm − . The N ex H correctedrelative intensities are plotted in Figure 6 (top panel).Note that Ar and Ca K α intensity ratios are slightlyhigher than canonical values and therefore require no N ex H . This result is consistent with the two other obser-vations. Since NGC 4151 does not show significant red-dening towards the narrow line region (Kraemer et al.2000), the varying outflow may be responsible for N ex H .In contrast to the other AGN, the Circinus galaxyrequires significant N ex H (Figure 4). The results arelisted in Table 2 and show a general agreement witheach other. If we assume Γ = 1 . . N ex H (Si) = (4 . ± . × cm − , or (4 . ± . × cm − for Γ = 1 .
8, which is in excellent agreement withdust extinction measurements in Circinus. Tristram et al. (2007) estimated the extinction in Circinus galac-tic foreground to be A V = 20 magnitudes which cor-responds to a column density of N H ≈ × cm − ,assuming N H ≈ A V × cm − . The N ex H correctedrelative intensities are plotted in Figure 6 (top panel)and match those predicted by I thickf well.We note that N H > cm − is the default assump-tion of the different AGN tori models. To fit Seyfert 2 X-ray spectra, these models require the torus to be clumpyto create unobscured lines of sight (Yaqoob 2012). To-tally unobscured cases where the Si/Fe K α intensity ra-tio is ∼ .
1, such as in NGC 1068, are therefore difficultto explain under these assumptions (Liu et al. 2016).The moderate N ex H values found above for all AGN arewell below the Compton-thick column of the torus.The situation for Vela X-1 is complicated and phasedependent. In the near eclipse observations (Eclipse, Preand Post) deviations from I thickf initially appears minor,whereas the other observations require significant N ex H corrections. This inconsistency hints at a more complexexplanation. Following Sako et al. (1999), the fluoresc-ing medium near eclipse is likely not optically thick andtherefore not well described by I thickf . Thus, we mustcalculate excess column density based on the full model(Equation (7)) rather than on I thickf (Equation (10)).Table 3 lists N ex H for the near eclipse Vela X-1 observa-tions using a fluorescing medium of N H = 2 × cm − .Table 4 lists N ex H for Vela X-1 phases 0.75, 0.5 and 0.15,calculated based on I thickf . As evident in the tables, a to-tal line of sight column density (interstellar and excess)of N tot H = 4 . ± . × cm − is roughly consistentacross phases and elements. In Figure 6 (bottom panel)we present the relative intensities for Vela X-1 observa-tions with N tot H = 4 × cm − .The most significant deviation from the I thickf ap-proximation is in GX 301-2, with each epoch requir-ing a different N ex H . The results are presented in Ta-ble 5. Note that the Galactic N H towards GX 301-2is already high at N H = 1 . × cm − . The esti-mates for N ex H for the IM and NA observations are eachroughly consistent between elements. At the IM phase N ex H (Si) = (5 . ± . × cm − and at the NA phase N ex H (Si) = (7 . ± . × cm − , which is consistentwith MAXI measurements of total N H (cid:46) cm − and N H ≈ ± × cm − for the IM and NA phases re-spectively (Islam & Paul 2014, Figure 5 therein).The N ex H values for the PP observation are higher(reaching 3 × cm − ), as expected for an XRB nearperiastron and as measured by Islam & Paul (2014).These measurements show a trend of N ex H increasingwith Z . A possible way to remedy this inconsistencyis with a flat power-law slope of Γ <
1. Indeed, Γ < N ex H (Si) in Circinus, GX 301-2 and VelaX-1. The overall agreement between the data and themodels is significantly improved over that of Figure 4.
12 14 16 18 20 22 24 26 28Atomic number Z10 -4 -3 -2 -1 R e l a t i v e I n t e n s i t y CircinusNGC 4151GX 301-2 IM GX 301-2 NAGX 301-2 PP
12 14 16 18 20 22 24 26 28Atomic number Z10 -4 -3 -2 -1 R e l a t i v e I n t e n s i t y Vela X-1 pre-eclipseVela X-1 eclipseVela X-1 post-eclipse Vela X-1 0.15Vela X-1 0.5Vela X-1 0.75
Figure 6.
Relative flux of K α fluorescence lines comparedto theoretical values after N ex H (Si) corrections. All fluxesare normalized relative to the flux of the Fe line. The blueline represents I thickf (Equation (10)). Top : The correctionworks particularly well for Circinus and the GX 301-2 IMand NA phases and less for the PP phase.
Bottom : Thecorrection works well for the Vela X-1 non-eclipse phases.For the eclipse phases a model of a fluorescing medium with N H = 2 × cm − is required (Equation (7), green line).. 6. DISCUSSIONExcess line of sight column density creates good agree-ment between the simple plane parallel models presentedin Section 4 and the data across many independent tar-gets and observations. Any minor remaining discrepan-cies between the data and models can be interpretedas variations in the few model assumption: ionizingspectrum, fluorescing medium N H , and elemental abun-dances. Such examples are shown above for Vela X-1( N H ) and GX 301-2 (Γ). Additionally, a more com-plex geometry may involve illumination-incidence andline-of-sight angles, which have a minor effect on the Table 2.
Line of sight excess column density ( N ex H ,Equation (15)) for the Circinus Galaxy and for theNGC 4151 combined observation. Element
Circinus Galaxy N ex H (10 cm − ) NGC 4151 N ex H (10 cm − ) Mg 4 . ± . . ± . . ± . . ± .
3S 7 . ± . . ± . . ± . . ± . Table 3.
Line of sight excess column density ( N ex H , Equation (15)) forthe Vela X-1 eclipse, pre-eclipse and post-eclipse phases, estimated basedon Equation (7) with N H = 2 × cm − . Element
Vela X-1(Eclipse) N ex H (10 cm − ) Vela X-1(Pre) N ex H (10 cm − ) Vela X-1(Post) N ex H (10 cm − ) Mg 3 . ± . . ± . . ± . . ± . . ± . . ± .
6S 3 . ± . . ± . < . . ± . < . < . < . < . < . Table 4.
Line of sight excess column density ( N ex H , Equation (15)) forVela X-1 phases 0.5, 0.75 and 0.15, estimated based on I thickf (Equation(10)). Element
Vela X-1(0.5) N ex H (10 cm − ) Vela X-1(0.75) N ex H (10 cm − ) Vela X-1(0.15) N ex H (10 cm − ) Mg 4 . ± . . ± . . ± . ± . . ± . . ± .
4S 4 . ± . ± . . ± . < . < . < . < . − − relative line intensities of Equation (10). An optimal fitobtained by varying all parameters is beyond the scopeof the present work.Special care should also be taken when interpreting re-sults from the Si K α measurement, where we accountedfor the blend with the H-like Mg Ly β (Section 3.1). Inour calculations, we assumed N ex H to affect only the fluo-rescence lines. In practice, this implies the near-neutraland ionized sources may have different line of sight col-umn densities. This result is supported by the GX 301-20 Table 5.
Line of sight excess column density ( N ex H , Equation (15)) forGX 301-2. Element
GX 301-2(IM) N ex H (10 cm − ) GX 301-2(NA) N ex H (10 cm − ) GX 301-2 (PP) N ex H (10 cm − ) Mg 3 . ± . . ± . − Si 5 . ± . . ± . . ± .
6S 5 . ± . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . observations, where the ionized emission lines are moreobscured than the fluorescence lines. In fact, the He-likeSi lines at ∼ . α is clearly visible at a longerwavelength.Figure 5 shows that Auger destruction cannot explainthe observed line intensities, as it needs to selectivelydestroy only florescence from low-Z elements. SelectiveAuger destruction might be possible if L-shell vacanciesexist in low-Z elements, but not in higher Z elements.This requirement limits the ionization parameter ξ toa narrow range. Based on Kallman & Bautista (2001),this range for selective Auger destruction up to and in-cluding Ca is 1 . < log( ξ ) < .
7, making this modelrestricted, but not impossible. The main problem; how-ever, with Auger destruction stems from the observa-tion of the nominal Fe K β line intensity. With selectiveAuger destruction, we would expect a decrease in theK β /K α line intensity ratio (Liedahl 2005), which is notobserved in any of the present spectra (see Section 3.2). CONCLUSIONSThe present work can be summarized as follows: • We surveyed the Chandra/HETG archive for allgrating spectra that feature at least four X-ray K α fluorescence lines in AGN and in Galactic XRB. • The K α intensity ratios between elements followsimilar trends in most observations, except for afew cases in which the low-Z lines (e.g., Mg, Si)are reduced by orders of magnitude (Figures 1,2). • For the most part, the relative K α intensities fol-low a simple plane-parallel approximation of adense, near-neutral optically-thick medium, de-fined as I thickf in Equation (10). The only two(sets of) free parameters in this model are theionizing spectrum and the elemental abundances(Figure 3). • The reduced K α intensities in the low-Z elementsis explained satisfactorily and self-consistently byexcess column density along the line of sight(Equation (15) and Figure 6). This excess col-umn derived here from the K α fluorescence lineratios is nicely corroborated by independent mea-surements, primarily reddening in AGN, and X-ray continuum absorption in XRB. Hence, X-rayfluorescence line ratios can provide an independentestimate of interstellar column density. • The K α intensity ratios do not show evidencefor resonant Auger destruction. Furthermore, theK β /K α intensity ratios are nominal, or even en-hanced, in all sources. This further indicates theK α fluorescing medium is near neutral.ACKNOWLEDGMENTSR. R. is supported by a Ramon scholarship from theIsraeli Ministry of Science and Technology. We acknowl-edge support by a Center of Excellence of THE ISRAELSCIENCE FOUNDATION (grant No. 2752/19). Wethank Ari Laor, Duane Liedahl, and Richard Mushotzkyfor helpful comments on the manuscript, and the highschool student Ahmad Ghanayim for searching and find-ing potential fluorescence line sources. Software:
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Table 6.
List of observations used
Object Observation ID Date observed Exposure (s) Notes
Circinus Galaxy 374 2000-06-15 7118Circinus Galaxy 62877 2000-06-16 60220Circinus Galaxy 4770 2004-06-02 55030Circinus Galaxy 4771 2004-11-28 58970Circinus Galaxy 10226 2008-12-08 19670Circinus Galaxy 10223 2008-12-15 102900Circinus Galaxy 10832 2008-12-19 20610Circinus Galaxy 10833 2008-12-22 28360Circinus Galaxy 10224 2008-12-23 77100Circinus Galaxy 10844 2008-12-24 27170Circinus Galaxy 10225 2008-12-26 67890Circinus Galaxy 10842 2008-12-27 36740Circinus Galaxy 10843 2008-12-29 57010Circinus Galaxy 10873 2009-03-01 18100Circinus Galaxy 10850 2009-03-03 13850Circinus Galaxy 10872 2009-03-04 16530NGC 1068 332 2000-12-04 45700NGC 1068 9148 2008-12-05 79540NGC 1068 9149 2008-11-19 88730NGC 1068 9150 2008-11-27 41080NGC 1068 10815 2008-11-20 19070NGC 1068 10816 2008-11-18 16160NGC 1068 10817 2008-11-22 32650NGC 1068 10823 2008-11-25 34540NGC 1068 10829 2008-11-30 38440NGC 1068 10830 2008-12-03 42900MRK 3 873 2000-03-18 100600MRK 3 12874 2011-04-19 77060MRK 3 12875 2011-04-25 29860MRK 3 13264 201-04-27 35760MRK 3 13263 2011-04-28 19720MRK 3 13261 2011-05-02 22080MRK 3 13406 2011-05-03 21430MRK 3 13254 2011-08-26 31530MRK 3 14331 2011-08-28 51210NGC 4151 335 2000-03-05 47440NGC 4151 7829 2007-03-19 49230NGC 4151 16089 2014-02-12 171900NGC 4151 16090 2014-03-08 68870GX 301-2 103 2000-06-19 39519 0.167-179 (IM)GX 301-2 2733 2002-01-13 39230 0.97-0.982 (PP)GX 301-2 3433 2002-02-03 59030 0.48-0.497 (NA)Vela X-1 102 2000-04-13 28010 0.015-0.051 : post-eclipse (Post)Vela X-1 1926 2001-02-11 83150 0.980 - 0.093 : eclipseVela X-1 1927 2001-02-07 29430 0.481-0.522 : 0.5Vela X-1 14654 2013-07-30 45880 0.748-0.807 : 0.75Vela X-1 18617 2017-02-21 44180 0.936-0.993 : pre-eclipse (Pre)Vela X-1 19953 2017-02-22 70470 0.132-0.223 : 0.15 Table 7.
Vela X-1 measured fluorescence line fluxes at various orbital phases
Element Rest Frame Photon Flux ( − ph s − cm − )Wavelength (˚A) Eclipse Pre-Eclipse Post-Eclipse 0.5 0.75 0.15 Mg 9.890 1 . +1 . − . . +1 . − . < . . +6 . − . . +2 . − . < . . +1 . − . . +2 . − . . +3 . − . +10 − . +4 . − . . +4 . − . S 5.373 17 . +3 . − . . +2 . − . +16 − +21 − . +8 . − . +11 − Ar 4.193 4 . +3 . − . . +2 . − . . +4 . − . +17 − +11 − +10 − Ca 3.359 9 . +3 . − . . +4 . − . . +5 . − . +30 − <
26 64 +17 − Cr 2.290 < . < . < . +66 − < < +12 − < < . < < < α ) 1.936 178 +17 − +28 − +28 − +150 − +77 − +70 − Fe (K β ) 1.757 23 +39 − +22 − <
24 1070 +230 − +123 − +105 − Ni 1.658 14 +13 − < <
27 260 +230 − +96 − < Table 8.
Measured fluorescence line fluxes for GX 301-2, Mrk 3, NGC 1068 and The Circinus Galaxy
Element Rest Frame Photon Flux ( − ph s − cm − )Wavelength (˚A) GX 301-2 IM GX 301-2 NA GX 301-2 PP Circinus Mrk 3 NGC 1068 Mg 9.890 1 . +2 . − . . +2 . − . < . . +0 . − . . +0 . − . . +1 . − . Si 7.126 8 . +1 . − . . +2 . − . . +2 . − . . +0 . − . . +0 . − . . +0 . − . S 5.373 22 +7 − +7 − . +4 . − . . +0 . − . . +1 . − . . +0 . − . Ar 4.193 9 . +4 . − . +10 − . +3 . − . . +0 . − . . +0 . − . . +0 . − . Ca 3.359 18 +6 − +23 − +9 − . +0 . − . . +0 . − . . +0 . − . Cr 2.290 <
15 57 +34 − +32 − . +1 . − . < . . +0 . − . Mn 2.102 23 +26 − < <
45 2 . +0 . − . . +1 . − . . +0 . − . Fe (K α ) 1.936 883 +59 − +100 − +270 − . +3 . − . . +3 . − . . +3 . − . Fe (K β ) 1.757 199 +81 − +135 − +250 − . +4 . − . . +3 . − . . +1 . − . Ni 1.658 <
64 180 +180 − +170 − . +3 . − . . +3 . − . < . Table 9.
Measured fluorescence line fluxes for NGC 4151
Element Rest Frame Photon Flux ( − ph s − cm − )Wavelength (˚A) 03-2000 03-2007 02-2014 03-2014 Mg 9.890 < . < . . +1 . − . . +1 . − . Si 7.126 8 . +2 . − . . +1 . − . . +1 . − . . +1 . − . S 5.373 5 . +7 . − . . +5 . − . . +2 . − . . +3 . − . Ar 4.193 <
14 6 . +3 . − . . +4 . − . < . +11 − . +4 . − . . +5 . − . +11 − Cr 2.290 <
490 8 . +8 . − . < . < . < < . < . < . α ) 1.936 202 +39 − +21 − +14 − +24 − Fe (K β ) 1.757 <
37 17 +17 − +13 − +28 − Ni 1.658 29 +32 − +21 − +11 − <<