GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L01104, doi:10.1029/2006GL028484, 2007
Atomic oxygen photoionization rates computed with high resolution cross sections and solar fluxes R. R. Meier,1 Brendan M. McLaughlin,2 H. P. Warren,3 and James Bishop3,4 Received 16 October 2006; revised 22 November 2006; accepted 7 December 2006; published 11 January 2007.
[1] Accurate knowledge of photoionization rates is fundamental for the study and understanding of gases in the solar system. Past calculations of the photoionization rates of atmospheric gases lack the spectral resolution to accommodate highly structured autoionization features in the photoionization cross section. A new theoretical model of the atomic oxygen photoionization cross section combined with a new solar minimum spectral irradiance model enables calculations at very high spectral resolution (0.001 nm). Our analysis of unattenuated photoionization rates reveals no strong coincidences among myriad bright solar emission lines and autoionization lines in the cross section. However, deeper in the terrestrial atmosphere, opacity effects are significant and the need for high spectral accuracy becomes increasingly important. In our solar minimum example, factor of 3 errors occur when the lower thermospheric photoionization rate of atomic oxygen is computed at 1 nm spectral resolution for both the cross section and solar flux. Citation: Meier, R. R., B. M. McLaughlin, H. P. Warren, and J. Bishop (2007), Atomic oxygen photoionization rates computed with high resolution cross sections and solar fluxes, Geophys. Res. Lett., 34, L01104, doi:10.1029/2006GL028484.
1. Introduction [2] Photoionization is an important process in the atmospheres of solar system objects. Hence, accurate knowledge of the ionization frequencies and rates throughout an absorbing atmosphere is vital for understanding its properties. Currently, calculations of photoionization rates use cross sections and solar fluxes at spectral resolutions less than desirable for full assessment of the impact of accidental resonances between highly structured features in their wavelength functions. The present study of atomic oxygen photoionization in the Earth’s atmosphere surmounts that limitation through use of physical models able to predict cross sections and solar spectra at unprecedented resolution. [3] The computation of solar energy deposition as a function of wavelength and altitude is the first stage in ab initio models that link observations of the solar EUV energy flux to observations of terrestrial atmospheric responses, including dayglow production. Photoelectron/dayglow 1 Department of Physics and Astronomy, George Mason University, Fairfax, Virginia, USA. 2 School of Mathematics and Physics, Queen’s University of Belfast, Belfast, UK. 3 E. O. Hulburt Center for Space Research, Naval Research Laboratory, Washington, DC, USA. 4 Deceased 30 December 2006.
Copyright 2007 by the American Geophysical Union. 0094-8276/07/2006GL028484
models such as GLOW [Solomon et al., 1988] and AURIC [Strickland et al., 1999] routinely use solar spectral irradiances and absorption cross sections evaluated at 0.1 nm resolution. But computationally intensive models such as global circulation models must operate with synthesized solar irradiances and ‘‘flux-weighted’’ cross sections that reduce wavelength array sizes from more than 1000 to some 20 – 40 (see Solomon and Qian [2005, and references therein] for examples). [4] A crucial assumption in all of these studies is that structure in the absorption and ionization cross sections is small within the adopted wavelength bin size. In the present paper, we test that assumption by investigating the degree to which wavelength resolution compromises the accuracy of computations of photoionization rates of atomic oxygen. This is only now made possible by the advent of new theoretical evaluations of the atomic oxygen photoionization cross section [Wilhelmi et al., 1999; McLaughlin, 2001] along with a new spectral irradiance model of the quiet Sun [Warren, 2005] that can be tabulated at unprecedented spectral resolution (0.001 nm) at wavelengths from 0.1 to 120 nm. [5] Such high resolution allows identification of overlaps between the many thousands of solar EUV emission lines and highly structured autoionization lines present in the O cross sectional models. Because autoionization lines have very narrow, large amplitude Fano line profiles, the cross section can frequently rise by two orders of magnitude or more above the continuum value, as well as drop significantly below the continuum, leading to very large increases or decreases in the ionization frequency in the vicinity of the lines. Self-absorption within autoionization lines also becomes important at low altitudes where the atomic oxygen concentration is large. The present analysis is limited to solar minimum conditions. (Extension of the new version of NRLEUV to higher levels of solar activity is under development.)
2. Atomic Oxygen Cross Section and Solar Flux Models [6] First principles theoretical modeling can provide photoionization cross sections at a much higher spectral resolution than is currently available experimentally. We have carried out such modeling using the R-matrix approach. For the valence region, the photoionization cross section calculations were performed with LS-coupling. We used an n = 3 basis set of physical orbitals determined by energy optimization on the state of interest. Thirty-four states of the resulting O+ arising from the 2s22p3, 2s2p4, 2s22p23l (l = s, p and d) configurations were included in the absorption model. Triple promotions from a limited set of
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Figure 1. Photoionization cross sections vs. wavelength. Present theoretical cross section (black), Fennelly and Torr [1992] compilation (red). (upper left) All wavelengths. Remaining panels show blowups of selected spectral regions. base configurations are used to describe the photoionization scattering model. Some 300 autoionization lines are present in the cross section. This type of model provides highly accurate theoretical results that compare favorably with experimental data for several other atomic systems [Schippers et al., 2003; Schlachter et al., 2004; Scully et al., 2006, and references therein]. In order to fully resolve all fine resonance structure we used an energy resolution of 136 meV. In the case of the K-shell region we utilized the high-resolution photoionization cross sections previously obtained by Gorczyca and McLaughlin [2000] that also include the effect of Auger linebroadening and agree well with recent high resolution synchrotron measurements. [7] Shown in Figure 1 is the computed O photoionization cross section for the full wavelength range (Figure 1, upper left) as well as for expanded intervals that illustrate the structure in more detail. The wavelength resolution of the cross section ranges from 104 nm at 25 nm to 103 nm at 91 nm. At even shorter wavelengths, the resolution varies from 105 nm in the structured region near the atomic oxygen K-edge around 2.4 nm, to 1 nm in the continuum. The red curves in Figure 1 are the commonly used Fennelly and Torr [1992] compilation (herein called FT). Their wavelength resolution is typically 0.1 nm for the solar continua, with finer resolution where solar emission lines are strong. The compilation is based on both laboratory measurements such as those of Angel and Samson [1988] and earlier theoretical computations. Some of the FT lines are located at wavelengths close to lines from the present theory, but are diluted due to low resolution. Other lines are displaced from the calculated cross section peaks. Some lines appear in our theory but not in the FT compilation; the converse is also true. In the former case, the laboratory measurements often lack sufficient wavelength resolution to isolate the many lines in the theoretical Rydberg series. In the latter case, the additional lines in the FT compilation may include features due the presence of molecular oxygen or metastable O in the laboratory systems. [8] Warren [2005] describes the features of the new solar minimum model and how it departs from earlier versions.
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The model uses a differential emission measure distribution calculated from spatially and spectrally resolved solar data at minimum solar activity and the CHIANTI database of atomic emission lines to derive the EUV spectral irradiance of the quiet Sun. The model, which contains some 50,000 emission lines and six continua, can be evaluated at any spectral resolution. For the present work, we have summed emissions in 0.001 nm bins. The solar emission line widths are typically of order 0.02 nm, but depend on a variety of factors, including motional broadening and opacity (e.g., see Dere and Mason [1993]). For the present work, we have computed photoionization rates at 0.001 nm resolution as well as with 0.02 nm FWHM Gaussian profiles imposed on emission lines (mean of the widths reported by Dere and Mason). We found that the rates have very little dependence on solar line width.
3. Photoionization Rates at High Spectral Resolution [9] The rate at which species i is photoionized at altitude z in the upper atmosphere (ionizations cm3s1) is defined as ji(z) = gi(z) ni(z), where gi(z) is the ionization frequency (s1) and ni(z) is the number density (cm3). The ionization frequency is t
Zi gi ¼
i ðÞFs ðÞe ðz;Þ d;
ð1Þ
0
where s is the photoionization cross section, lti is the wavelength threshold for photoionization for species i, Fs(l) is the solar spectral irradiance (photon cm2s1nm1), and t is the optical depth at wavelength l between altitude z and the Sun. The optical depth is ðz; Þ ¼
X i
ai ðÞ
Z1
ni ðz0 Þds;
ð2Þ
z
where a designates total absorption and s is the distance along the path to the Sun. For an overhead Sun, s = z0. The computation of the ionization frequency is carried out by mapping the O, N2 and O2 cross sections (and the optical depths) to the center of discrete 0.001 nm solar wavelength bins and summing the bins. It is not necessary to account for Doppler broadening of the O autoionization lines because the terrestrial line width is much smaller than the solar line widths. [10] Figure 2 presents details of the O photoionization frequency at the top of the atmosphere (t = 0), obtained using the NRLEUV solar minimum spectral irradiance shown in blue (Figure 2, top) and the photoionization cross section (s) shown in green. The spectral irradiance is defined as the total number of photons cm2 s1 within 0.001 nm wavelength bins (integral of Fs over a bin) between 0.1 and 91.044 nm; the cross section is evaluated at the center of each bin. Figure 2 (bottom) displays the ionization frequency, g, for each wavelength bin. The cumulative ionization frequency (black line) beginning at the shortest wavelength provides a comparative view of how individual bins contribute to the total. A strong
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Figure 2. (top) NRLEUV solar minimum spectral irradiance in 0.001 nm bins vs. wavelength (blue); use left axis. Photoionization cross section vs. wavelength (green); use right axis. (bottom) Photoionization frequency in 0.001 nm bins vs. wavelength (red). Cumulative photoionization frequency vs. wavelength (black) beginning at shortest wavelength. coincidence between a solar line and peak in the photoionization cross section would produce a noticeable step in the cumulative rate. No strong accidental resonances are evident, even though autoionization lines soar above or plunge below the ionization continuum level, promoting or demoting the contributions of solar ionizing radiation at their wavelengths. The various step changes seen in the cumulative rate, e.g., at He II 30.4 nm, are actually due to bright solar lines and not to enhancements from autoionization lines in the cross section. [11] We note that the total ionization frequency at the top of the atmosphere, obtained by summing the cumulative ionization frequency over all wavelengths, is 2.94 107 s1. If the FT cross section is used instead, the total ionization rate becomes 2.85 107 s1. Both values are within the range of low resolution, quiet Sun values referenced in the compendium by Huebner et al. [1992]. [12] Although our high resolution analysis suggests that accidental coincidences between solar and cross section lines do not induce significant uncertainties in calculations of the quiet Sun photoionization rate with lower spectral resolution, a somewhat different picture emerges when the effect of extinction on the altitude dependence of the ionization rate is taken into account. For illustration we chose a solar minimum model atmosphere (NRLMSIS 2000E-00 evaluated at F10.7 = 75, latitude = 23°, longitude = 0°, solar zenith angle = 45°, Ap = 1; exospheric temperature = 785 K [Picone et al., 2002]) to calculate the atomic oxygen photoionization rates at different altitudes in the Earth’s atmosphere. [13] For computation of photoionization rates throughout the ionosphere, we use the Fennelly and Torr [1992] O2 and N2 total absorption cross sections to account for extinction of sunlight by those species. Their compilation is probably sufficient to resolve the broad structure in the molecular absorption cross sections at wavelengths shorter than the O ionization limit (this work), but certainly not in the highly
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structured regions leading up to the O2 ionization limit (to be addressed in future work). [14] Figure 3 displays the atomic oxygen photoionization rate, jO(z) = gO(z) nO(z), as a function of altitude for three cases. The highest resolution case (at 0.001 nm) is shown in black. In the next case (red curve), the solar flux is averaged over 0.1 nm bins and the ionization cross section (and each absorption cross section) is evaluated at the center of the bin. The third case (blue curve) also uses the 0.1 nm binned solar flux, but the bin center O cross section is instead from FT. The dashed curves (upper scale) represent the ratios of the latter two (binned) cases to the high resolution case. We see that averaging the solar fluxes over 0.1 nm bins and using bin-center cross sections results in errors that approach +40% near 110 km, but drop below the high resolution case at higher and lower altitudes. The nonmonotonic behavior evident in the ratios in Figure 3 is due to four competing effects in the ionization frequency (equation (1)): (1) the dramatic rise in the cross section on one side of an autoionization line causes the ionization frequency to increase above the continuum, but (2) the large cross section also produces a significant increase in the portion of the optical depth due to atomic oxygen (equation (2)), thereby lowering the ionization frequency; (3) the valley in the cross section on the other side of an autoionization line reduces the ionization frequency, but (4) the low cross section there reduces the optical depth, thereby allowing greater penetration of solar radiation that in turn increases the ionization frequency. While bin-averaging smoothes the solar spectral structure, choosing cross sections at bin centers retains some structural character. [15] If the cross sections as well as the solar irradiances are bin-averaged, the behavior of the photoionization rate relative to the high resolution case becomes qualitatively different. Figure 4 (left) shows the ratios (as defined in Figure 3) as functions of altitude. Now the FT rates are below the high resolution case everywhere except at the lowest altitudes. Near 120 km, the binned evaluations are 30% below the high resolution case and about a factor of two lower than if the cross sections are evaluated at bin centers.
Figure 3. Photoionization rate vs. altitude (solid lines). 0.001 nm solar flux bins with present theoretical cross section (black), 0.1 nm solar flux bins with present theoretical cross section (red), and 0.1 nm solar flux bins with FT compilation (blue). Cross sections have been evaluated at bin centers. Dashed curves are latter cases divided by the 0.001 nm bin case (use upper scale for ratios).
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Figure 4. Ratio of photoionization rates to 0.001 nm solar flux bin case with cross sections averaged over bins. (left) 0.1 nm solar flux bins with present theoretical cross section (red), and 0.1 nm solar flux bins with FT compilation (blue). (right) 1 nm solar flux bins with present theoretical cross section (red), and 1 nm solar flux bins with FT compilation (blue).
[16] The accuracy of the photoionization rate computations worsens considerably if the bins are widened to 1 nm, the resolution at which SEE solar spectral irradiances are routinely reported [Woods et al., 2005]. When using binaveraging for both the solar flux and the cross sections bins, Figure 4 (right) shows that both binned rates at 120 km are about a factor of 3 lower than the high resolution case.
4. Discussion [17] Evaluation of photoionization frequencies at the top of the Earth’s atmosphere using a modeled quiet Sun irradiance with almost 50,000 optically thin emission lines between 0 and 120 nm and a theoretical O photoionization cross section containing more than 300 autoionization lines reveals no strong resonances between bright solar emission lines and autoionization lines in the cross section. Certainly weaker accidental resonances do occur, but they have little individual influence. This conclusion is, of course, restricted to solar minimum, quiet Sun conditions. It is possible that some solar lines that overlap cross sectional structure will intensify significantly at solar maximum or during flares and exert greater influence. High solar activity spectral irradiance models are under development and should resolve that issue in the near future. [18] Moving deeper into the terrestrial atmosphere, the need for high spectral accuracy becomes increasingly important as higher and lower opacity effects compete with lower and higher structure in the cross section autoionization lines, respectively. If photoionization rate calculations are carried out at lower spectral resolution, important errors emerge as crucial structure is diluted. For example, rates calculated at 1 nm spectral resolution have errors of a factor of 3 in the lower thermosphere. Although no solar spectral irradiance measurements at 0.001 nm resolution over the entire band shortward of 91 nm are foreseen in the near future, there may be appropriate ways to use carefully selected spectral bands with flux-weighted cross sections that reproduce rates computed at very high resolution. Solomon and Qian [2005] and others have investigated this approach at much lower spectral resolution for employment by computationally intensive global circulation models. It
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remains to be seen how well this approach works in the very high resolution domain. We will investigate the potential of this parameterization when the solar spectral model is extended to other levels of solar activity. [19] As noted, with the present high resolution solar spectrum and atomic oxygen cross section, we found no strong accidental resonances between solar lines and cross section lines. However, the wavelengths of the autoionization lines in the cross section need to be established with even greater precision. While some of the theoretical and observed line positions are well within a fraction of a nanometer, others are displaced by amounts greater than experimental error. It is possible that some of the experiments are contaminated by metastable oxygen atoms or O2. As well, improvements in wavelength resolution, calibration and other experimental conditions, as noted by Angel and Samson [1988], may well lead to better agreement with theory. Wavelengths of theoretical cross section lines should also become more accurate with enhanced basis functions that are used to approximate the state wave functions. [20] The next phase of this work will include extension to solar maximum and flare conditions, when we expect additional strong solar emission lines to emerge. As well, we plan to incorporate the new O cross sections and solar fluxes into the AURIC code in order to compare with the lower spectral resolution approximations currently used to compute photoelectron fluxes, and electron and ion densities. We will also investigate the accuracy of O2 photoionization rate calculations, which are suspect because the highly structured N2 absorption cross section between 91 nm and the O2 ionization limit at 102.715 nm is approximated in extant compilations by smooth wavelength functions. As with atomic oxygen, serious errors may result if atmospheric transmission of solar emission lines through the highly structured optically thick N2 absorption lines is not taken into account. [21] Acknowledgments. RRM thanks NASA for support from the TIMED Guest Investigator Program. JB thanks the Office of Naval Research for support. HPW was supported by the NASA Living With a Star Program and the Office of Naval Research.
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Schlachter, A. S., et al. (2004), Lifetime of a K-shell vacancy in atomic carbon created by 1s ! 2p photoexcitation of C+, J. Phys. B At. Mol. Opt. Phys., 37, L103. Scully, S. W. J., et al. (2006), Doubly excited resonances in the photoionization spectrum of Li+: Experiment and theory, J. Phys. B At. Mol. Opt. Phys, 39, 3957. Solomon, S. C., and L. Qian (2005), Solar extreme-ultraviolet irradiance for general circulation models, J. Geophys. Res., 110, A10306, doi:10.1029/ 2005JA011160. ˚ Solomon, S. C., P. B. Hays, and V. J. Abreu (1988), The auroral 6300 A emission: Observations and modeling, J. Geophys. Res., 93, 9867. Strickland, D. J., J. Bishop, J. S. Evans, T. Majeed, P. M. Shen, R. J. Cox, R. Link, and R. E. Huffman (1999), Atmospheric Ultraviolet Radiance Integrated Code (AURIC): Theory, software, architecture, inputs, and selected results, J. Quant. Spectrosc. Radiat. Transfer, 62, 689. Warren, H. P. (2005), A solar minimum irradiance spectrum for wavelengths below 1200 A, Astrophys. J. Suppl. Ser., 157, 147. Wilhelmi, O., G. Mentzel, B. Zimmermann, K.-H. Schartner, H. Liebel, H. Schmoranzer, and B. M. McLaughlin (1999), Absolute cross sections
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for the photoionization of atomic oxygen: 2s-electron ionization and satellite production in the threshold energy range, Phys. Rev. A, 60, 3702. Woods, T. N., F. G. Eparvier, S. M. Bailey, P. C. Chamberlin, J. Lean, G. J. Rottman, S. C. Solomon, W. K. Tobiska, and D. L. Woodraska (2005), Solar EUV Experiment (SEE): Mission overview and first results, J. Geophys. Res., 110, A01312, doi:10.1029/2004JA010765.
H. P. Warren, E. O. Hulburt Center for Space Research, Naval Research Laboratory, 4555 Overlook Avenue SW, Washington, DC 20375, USA. B. M. McLaughlin, School of Mathematics and Physics, Queen’s University of Belfast, Belfast BT7 1NN, UK. R. R. Meier, Department of Physics and Astronomy, George Mason University, 4400 University Drive,MS 3F3, Fairfax, VA 22030, USA. (
[email protected])
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