LETGS: Carbon

Jeremy J. Drake (Smithsonian Astrophysical Observatory)

Jeremy Drake

Carbon. It’s everywhere these days. Popularized by the spewing chimneys of the industrial revolution, and explained by Fred Hoyle’s 12C resonance that facilitates Bethe’s triple-alpha process in stellar nucleosynthesis. They make everything with it now: aeroplanes, racing cars, bicycles, tennis rackets, musical instruments, footprints, everything. They even use it to make optical blocking filters for X-ray satellites. But despite its moderately important role as the basis of life as we know it, carbon still has a bit of an image problem. This is perhaps partly due to it being the prime constituent of “smut”, which X-ray instrument builders refer to euphemistically as “contamination”. It doesn’t help that carbon also proves to be rather messy under the X-ray microscope of high-resolution spectroscopy.

 Like all heavy elements, the X-ray transmittance of carbon near its ionization threshold, between about 40 and 45 Å (0.3–0.28 keV), shows complex X-ray absorption near-edge structure (XANES). This would be all well and good—we could use this structure as a spectroscopic tool to study carbon in the cosmos, as has been done for elements such as O, Ne and Fe (Juett et al. 2004, 2006)—were it not for our carbon filter-clad instruments showing the same structure. It’s not quite the same structure though, and this makes it all the more messy.

The optical and UV blocking filters on the Chandra detectors are made from aluminium-coated polyimide. The polyimide (C22H10N2O5) substrate in these metal-polymer foils provides the flexural and tensile strength needed for the filter to survive the rigors of launch, while the carbon also helps attenuate UV and optical light. The energies of inner-shell states in carbon whose valance electrons are bound up in a polymer such as this are perturbed relative to those in isolated carbon atoms. The detailed structure and energies of absorption resonances of a given element then depend on its ionization and chemical state. Accurate calculation of this photoabsorption cross section for complex materials such as polyimide is currently not readily tractable, and consequently, the ACIS and HRC filter transmittances as a function of wavelength used to construct the Chandra effective areas are based on measurements obtained in the laboratory and at synchrotron facilities. These calibration measurements do a pretty good job of matching most of the resonance features seen near the carbon edge in LETG observations. Pretty good because for many sources the filter signature dominates, but we would not expect a perfect match because of carbon absorption in the source and in the intervening interstellar medium.

While detailed photoabsorption cross sections complete with resonance structure cannot yet be readily computed for complicated chemical compounds, they can be computed for single atoms and ions. Indeed, the use of K-edge resonance structure for studying elements like O and Ne in the ISM was made possible by such computations (García et al. 2005; Gorczyca 2000). Similar calculations for carbon should, at least in principle, enable the same sort of studies for C to be made. Moreover, an accurate cross section for the cosmic absorbers should provide a check on the propriety of the instrument absorption features and calibration in the vicinity of the edge.

Such calculations were taken on by Tom Gorczyca and his graduate student, Fatih Hasoglu, at Western Michigan University (Hasoglu et al. 2010). An example of how the resulting cross sections look is illustrated for C II in Figure 1; similar calculations were performed for C II, III and IV ions. Also shown in Figure 1 is the cross section computed using an independent particle approach—essentially a mean-field approximation in which the detailed interactions of the 1s electron under consideration with other electrons in the ion are not taken into account. These more simplified cross sections are characterized by ionization edges that are essentially a step-function at the ionization threshold, and are similar to those included in ISM X-ray absorption models in common use. The resolving power of the LETGS at these energies is about 1000—0.3 eV or so—and it might be appreciated by the comparison that the resonance structure will have an impact on observations for sources in which the cosmic absorption component becomes comparable to that of the filter.

Fig. 1.— C II photoabsorption cross section from detailed calculations carried out by Fatih Hasoglu and co-workers, compared to the earlier simplified independent-particle approach results of Reilman & Manson (1979). From Hasoglu et al. (2010).

We turned to our trusty blazar calibration source, Mkn 421, to test an ISM absorption model using the new high-resolution C cross sections. This source was caught in a very high state during an LETG+HRC-S observation on 2003 July 1 and 2 (ObsID 4149; see Nicastro et al. 2005 for a full description). An absorbed power-law continuum model has never produced a really good fit to this spectrum in the vicinity of the main C resonances. Trying a fit with an ISM absorption model that included the new high-resolution C cross sections was instead quite revealing. The fit used a power-law continuum with photon index  Γ = 2 and ISM absorption corresponding to cosmic metal abundances and neutral hydrogen column density of N(H)  = 1.5 ×1020 cm-2—slightly different to the parameters adopted by Nicastro et al. (2005), but here we optimized the fit to the C edge region. Immediately apparent was a precise coincidence between the C II 1s2s22p2 (2S, 2P, 2D) resonances and a discrepancy in the same fit performed using the step function edge employed in the Balucinska-Church &McCammon (1992) absorption model. The redshift of the C II absorber is zero, indicating that it resides along the line-of-sight in our Galaxy. The new C model could not help a 5%–15% under-prediction of the data in the 42–44 Å range though, but since this was just an informal test and most readers will never read this far into the article, we just cheated a bit and added a broad Gaussian-like correction to the effective area to fix it. The fraction of the ISM carbon to put among the different C charge states could then be done using rigorous statistical methods. It could be, but I just did it by eye and got 20% C I, 60% C II, and for good measure, 20% C III. This fit is illustrated in Figure 2, together with one using the Balucinska-Church & McCammon (1992) step function absorption model. The new high resolution photoabsorption cross-section data for carbon are available from Tom Gorczyca on request (thomas.gorczyca@wmich.edu).

Fig. 2.— Carbon K-edge region of the X-ray spectrum of the bright blazar Mkn 421 observed by the Chandra LETG+HRC-S. The edge absorption is mostly due to the polyimide UV optical/ion blocking filter on the HRC-S instrument, although ISM absorption contributions are also present. Two fits to a power-law continuum model with photon index Γ = 2.0, absorbed by an intervening ISM corresponding to a neutral H column density of 1×1020 cm-2, are shown. These differ significantly only in the carbon cross sections employed: the neutral C I cross section of Balucinska-Church & McCammon (1992); and the CI, C II, and C III cross sections containing detailed resonance structure. In the latter case, the C ion fractions were 20% C I, 60% C II, and 20% C III. The effect of the C II resonances is clearly visible in the vicinity of 43 Å. From Hasoglu et al. (2010).

So, the improvement in the fit is perhaps not so dramatic? Keep in mind that the ISM column toward Mkn 421 is very low compared with most Galactic lines of sight that will exhibit much stronger ISM features. We still need to look in more detail at the broad Gaussian cheat in the 42–44 Å region to determine if it really does warrant inclusion in the instrument calibration, or if it might be explained by other means. Any calibration updates for the region close to the C edge will likely be included later in the year, together with planned revisions to the HRC-S quantum efficiency at λ > 44 Å. There is also a weak absorption feature near 42.15 Å in the observed spectrum suggestively close to the predicted C II 1s2s22p2 (2S, 2P, 2D) resonances that bears further study; absence of a stronger feature tells us that at most only about 20% of the carbon in the line-of-sight is in the form of C(2+): galactic interstellar smut is not highly-charged.

REFERENCES

Balucinska-Church, M., & McCammon, D. 1992, ApJ, 400, 699 (abstract)

García, J., Mendoza, C., Bautista, M. A., Gorczyca, T. W., Kallman, T. R., & Palmeri, P. 2005, ApJS, 158, 68 (abstract)

Gorczyca, T. W. 2000, Phys. Rev. A, 61, 024702 (abstract)

Hasoglu, M. F., Abdel-Naby, S. A., Gorczyca, T. W., Drake, J. J., & McLaughlin, B. M. 2010, ApJ, 724, 1296 (abstract)

Juett, A. M., Schulz, N. S., & Chakrabarty, D. 2004, ApJ, 612, 308 (abstract)

Juett, A. M., Schulz, N. S., Chakrabarty, D., & Gorczyca, T. W. 2006, ApJ, 648, 1066 (abstract)

Nicastro, F., et al. 2005, ApJ, 629, 700 (abstract)

Reilman, R. F., & Manson, S. T. 1979, ApJS, 40, 815 (abstract)

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2 Responses to LETGS: Carbon

  1. Sultana N. Nahar says:

    I would make the comment that the same resonant structures seen near the K-edge photoionization cross sections for carbon computed by Hasoglu
    et al. (2010) were shown 10 years ago in Fig. 1(c) of “ELECTRON-ION
    RECOMBINATION RATE COEFFICIENTS AND PHOTOIONIZATION CROSS SECTIONS FOR ASTROPHYSICALLY ABUNDANT ELEMENTS. IV. RELATIVISTIC CALCULATIONS FOR C IV AND C V FOR ULTRAVIOLET AND X-RAY MODELING” by Nahar, Pradhan, Zhang, ApJS 131, 375 (2000). These structures remain about the same in about the same photoelectron energy range regardless the ionization state of the element.

  2. Brendan McLaughlin says:

    Hi Sultanna/Claudio/Manuel,
    I would like to make the following comments.

    In the theoretical work by Pradhan, Nahar and co-workers on Li-like (C IV, O VI and Fe XXIV) Nahar S N, Pradhan A K, Zhang H L 2001 (Phys. Rev. A 63 060701); RR+DR (C IV) Pradhan A K, Chen G X, Nahar S N and Zhang H L 2001 (Phys. Rev. Lett. 87 183201); and RR+DR, PI (C IV, C V) Pradhan A K, Nahar S N and Zhang H L 2000 (ApJ. Suppl. Ser. 131 375) done over a decade ago, only C IV (C3+) and C V (C4+) were investigated in those papers. The limitations of that early K-shell work have been addressed in the high-resolution experimental data taken at the ALS with Alfred Mueller’s group, and benchmarked with theory and the data taken from the Stockholm CRYRING. Please see our paper on C3+ [K-shell] Mueller et al J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 235602 for a complete discussion on the accuracy of theory and experiment.

    I would also like to draw your attention to the fact that, in the X-ray spectrum of the bright blazar Mkn 421 observed by the Chandra LETG+HRC-S, those ions weren’t seen in the Chandra spectra. The main focus of the work by us [Hasoglu et al. (2010)] was on neutral and singly ionized carbon at the K-edge since it is the resonance features from these that dominate the spectra.

    As noted in our paper, very little if any experimental or theoretical work was available, particularly on neutral carbon to benchmark theory, prior to our work at the K-edge. The energy range of the experimental work (from the ALS) on the rest of the Carbon isonuclear sequence is limited to the n=2 and 3 resonance region below the K-edge. What high resolution experimental work that does exist over the various energy ranges has already been benchmarked in a series of papers with Alfred’s group: C+ [K-shell] Scully et al J. Phys. B: At. Mol. Opt. Phys. 37 (2004) L103–L109; C2+[K-shell] Scully et al J. Phys. B: At. Mol. Opt. Phys. 38 (2005) 1967–1975; C3+[K-shell] Mueller et al J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 235602; and more recently, on Li-like B2+ ions: B2+ [K-shell] Mueller et. al. J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 135602.

    I would also draw your attention to a comparison between our published
    neutral Carbon K-shell cross section data [Hasoglu et al. (2010)] and the data available on your website. As one can clearly see, there is over an order of magnitude discrepancy between the two data sets. The fact that our data set has been benchmarked with the observed spectrum from the bright blazar Mkn 421 observed by the Chandra LETG+HRC-S, reproducing all the features in the observations, gives further confidence in our work. This has been pointed out by Jeremy Drake above.

    For your edification, all our data is stored at the website http://tesla.physics.wmich.edu/ResearchResults.php?PG=2&SC=5

    Cordially yours
    Brendan McLaughlin

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