Fe IX Calculations for the Solar Dynamics Observatory
aa r X i v : . [ a s t r o - ph . S R ] S e p Fe IX Calculations for the Solar Dynamics Observatory
Adam R. Foster and Paola Testa
Smithsonian Astrophysical Observatory, 60 Garden Street, Cambridge, MA 02138 [email protected]
ABSTRACT
New calculations of the energy levels, radiative transition rates and collisionalexcitation rates of Fe ix have been carried out using the Flexible Atomic Code,paying close attention to experimentally identified levels and extending existingcalculations to higher energy levels. For lower levels, R-matrix collisional exci-tation rates from earlier work have been used. Significant emission is predictedby these calculations in the 5f-3d transitions, which will impact analysis of SDOAIA observations using the 94˚A filter. Subject headings:
Atomic Data — Sun: UV radiation
1. Introduction
The launch of the Solar Dynamic Observatory (SDO) allows observation of the Sunin unprecedented detail. The Atmospheric Imaging Assembly (AIA, Lemen et al. (2011))provides multiple simultaneous images of the solar disk every 12 seconds, taken through avariety of narrowband filters centered on individual emission lines of interest. One such filterin centered on 94˚A, and targets both the Fe xviii (93.923˚A) transition from 2s S / → P / at high temperatures and the Fe x (94.012˚A) line from the 3p D / → P / transition in cooler plasma. The emission from these two lines occurs in verydifferent temperature ranges and therefore can be distinguished if the plasma temperaturedistribution is known (Boerner et al. 2011).Lepson et al. (2002) observed spectra of Fe vii to Fe x using an electron beam iontrap (EBIT) and a grazing incidence spectrometer with resolution of ≈
300 at 100˚A toobserve lines in the 60 to 140˚A range. They estimated that 70% of the emission in this bandwas unaccounted for by the existing atomic data in the mekal (Kaastra & Mewe 1993;Mewe, Kaastra & Liedahl 1995) database. Since then, none of the major atomic databases(e.g. chianti (Dere et al. 2009), AtomDB (Foster et al. 2011), nist (Ralchenko et al. 2011), 2 –and the successor to mekal , spex (Kaastra, Mewe & Nieuwenhuijzen 1996)) have updatedtheir atomic data for Fe ix to include any lines in this region. Of particular interest are twoFe ix lines, observed at 93.59 and 94.07˚A, which both fall in the bandpass of the 94˚A AIAfilter.These lines were identified by comparing the EBIT results with calculations using the He-brew University Lawrence Livermore Atomic Code ( hullac , Bar Shalom, Klapish & Oreg(2001)) as belonging to the 3p → transitions of Fe ix . The structure and col-lisional calculations of the current version of chianti , version 6.0.1 (and, by extension,AtomDB which uses the chianti data for this ion) only include configurations up to the n=4principal quantum shell, and therefore omit these transitions. The NIST (Ralchenko et al.2011) database does include some n=5 transitions but not these lines or levels.In this work, we have carried out calculations using the Flexible Atomic Code (FAC,Gu (2003)) to extend the energy level and collisional calculations to include higher energylevels up to the n=6 shell, merged the resulting data with the best available collisional andradiative data for lower levels, and used the collisional-radiative code apec (Smith et al.2001) to model the resulting emission and therefore the effect on the AIA 94˚A filter flux.
2. Method
The NIST atomic spectra database (Ralchenko et al. 2011) lists 35 observed energylevels for Fe ix , including the lowest 17 energy levels and 18 others up to the 3p level.Solar observations using the HINODE/EIS instrument have led to the identification of fourmore energy levels: 3p G [4 , , and 3p S (Young 2009).Theoretical calculations of the Fe ix structure have been performed by several groups.The configurations included in some of these are listed in Table 1. Storey, Zeippen & Le Dourneuf(2002) performed superstructure (Eissner, Jones & Nussbaumer 1974) calculations ofthe first 140 energy levels combined with an R-Matrix collision calculation. Aggarwal et al.(2006) revisited this using the General Purpose Relativistic Atomic Structure Package (GRASP,Dyall (1989)) and FAC to calculate energy levels and transition rates. They used variousconfiguration combinations in order to match the first 17 energy levels as closely as possible,while also paying particular attention to the first 360 energy levels. They found that theeffect of the CI between many of the configurations on the energy levels and subsequentoscillator strength calculations is of importance, in particular the 3s . This was omit-ted during another set of calculations by Verma et al. (2006) using the civ3 (Hibbert 1975)code, and gave very different results compared to those of Aggarwal et al. (2006) and ob- 3 –Table 1. The configurations included in previous caclulations of energy levels, A-valuesand collision strengths of Fe ix . S2002 denotes the Storey, Zeippen & Le Dourneuf (2002)data while A2006 denotes Aggarwal et al. (2006). Levels marked “CI” are included only forconfiguration interaction purposes.Config. S2002 A2006 Current Config. S2002 A2006 Current3s Y Y Y 3s CI Y Y3s Y Y Y 3s CI3s Y Y Y 3s Y Y Y3s Y Y Y 3s Y Y3s CI Y Y 3s CI3s Y Y 3s CI3s Y 3s CI Y Y3s Y 3s Y CI3s Y Y Y 3s CI3s Y Y 3s CI3s CI 3s CI Y CI3s CI 3p CI Y CI3s CI 3p CI CI 4 –served energy levels. The configurations listed in Table 1 are those from their best fittingGRASP run.The energies of Storey, Zeippen & Le Dourneuf (2002) agree with the observed energiesto within 6% (the energies of the first 17 levels were set to match observed values after thestructure calculation was complete), while those of Aggarwal et al. (2006) agree within theobserved energies 1 to 3%. The exception to this are the four levels from (Young 2009),numbers 94, 95, 96 and 144 in our energy ordering. These were not identified until after theAggarwal et al. (2006) data was created, and there is a substantial difference in both theenergies and the level ordering caused by their introduction (see Figure 1).In our FAC calculation, we have experimented with different configuration sets to obtaina good match with the observed energies in both absolute energy and energy level ordering,and to include the higher n shells from which the emission takes place. We have included the3s and 3s configurations to include the higher n emission which we are tryingto characterize.We have also included many other configurations for their CI effects. The couplingbetween configurations of the same parity can affect the energy ordering of many of the levelsduring the structure calculation. In this case, most of these levels do not contribute observedemission lines, and their energies are much higher than those of immediate spectroscopicinterest for which there are observed lines ( > and 3s configurations in the structure calculation which adds the CI necessary to bring the energiesof the Young (2009) levels back to within 2.5% of the observed values, and also creates anenergy ordering which matches observations for all identified levels. Using our much largerFAC calculation, we obtain values comparable to those of Aggarwal et al. (2006) for thelower energy levels and again within 1 to 2.6% of observed values at higher levels. This doeslead to significant changes in the energy ordering of levels when compared to the calculationsof Aggarwal et al. (2006). Our energy levels, combined with our best attempts to identifymatching levels have been listed in Table 2.We note (see Figure 1) that our calculated energies are without exception higher than theobserved values. This offset scales simply with energy, resulting in calculated levels which are1-2.5% larger than observed values. Since the goal of these calculations is to produce useful 5 – O b s e r v e d E n e r gy / C a l c u l a t e d E n e r gy Level Index
SSGRASPCurrent
Fig. 1.— The ratio of the observed and calculated energies for Fe ix levels from a varietyof methods. Squares: superstructure (Storey, Zeippen & Le Dourneuf 2002); circles:GRASP (Aggarwal et al. 2006); stars: this work. The levels with observed energy levelsfrom hinode observations (Young 2009) are highlighted, as is the 1% to 3% difference bandin which all the current results fall. The dashed line indicates the correction factor usedfor all higher energy levels. A description of these levels is in Table 2, with their indexes incolumn 5. Only those levels with observed counterparts are included. 6 –Table 2. The list of energy levels resulting from this work. E F AC refers to the originalresults from FAC calculations, E corr are the energies after correction as described in thetext. For each level with an observed energy value, the index of this level in Figure 1 isgiven ( Ind fig ): for these levels E corr = E observed . For comparison, the grasp results ofAggarwal et al. (2006) are listed ( E G ), along with the energy order from that work (Ind G ).A star denotes a level for which a different configuration is found between our work andAggarwal et al. (2006).Index jj Symbol E
FAC E corr Ind
Fig.1 E G Ind G (eV) (eV) (eV)1 3p (0 , (cid:0) , , (cid:1) (cid:0) , , (cid:1) (cid:0) , , (cid:1) (cid:0) , , (cid:1) (cid:0) , , , (cid:1) (cid:0) , , , (cid:1) (cid:0) , , , (cid:1) (cid:0) , , (cid:1) (cid:0) , , , (cid:1) (cid:0) , , (cid:1) levels of primary interest in this work are of ahigher energy than any other experimentally identified levels of Fe ix . Noting the relativelyuniform overestimate of the energy in the structure calculations, we have scaled the energiesfor all levels above the highest observed energy level by the mean of the adjustment usedfor experimentally identifed levels, 0.9817. The observed energy levels are the 17 levels fromNIST, the 4 levels from Young (2009), and four levels calculated from the Lepson et al.(2002) measurements: (3p ) (E=163.2eV), (3p ) (E=164.9eV), (3p ) (E=188.9eV), (3p ) (E=189.6eV).Radiative rates were calculated by Aggarwal et al. (2006) based on their structure cal-culation. We have initially attempted to use these radiative rates, however the significantdisagreements in the energy level ordering have made this problematic for most levels. Wehave therefore used the Aggarwal et al. (2006) values for transitions among the lowest 17energy levels, where the ordering is definite, and the remainder have been calculated usingthe relativistic method within FAC.Storey, Zeippen & Le Dourneuf (2002) performed R-Matrix calculations, producing col-lisional excitation rates among the lowest 140 energy levels. Further work was performedusing FAC by Liang et al. (2009), although again these did not incorporate n=5 configura-tions.A full R-matrix calculation including all of the excited levels on the n=5 level wouldbe a prohibitively large calculation and is beyond the scope of this work. We have thereforeuse the distorted wave FAC collision code to calculate collision strengths between all of thelevels of Fe ix included in our structure calculations. The advantage of this approach isthe fast production of results and the inclusion of large numbers of levels. The downsideis the omission of low-energy resonance effects, which can be significant. We therefore usethe R-matrix collision strengths of Storey, Zeippen & Le Dourneuf (2002) where they exist.We note that the problem of matching levels between the calculations persists. For mostlevels, we have matched the levels with the same electron configuration and total angularmomentum, J , and then paired these results in energy order. For the 3p and 3p levels there are different numbers of levels (for the former configuration, our calculationhas 2 more levels for each of J =2, 3 and 4; for the latter Storey, Zeippen & Le Dourneuf(2002) have 2 more). We have therefore combined these two configurations, which overlapcompletely in energy at the higher end of the 3p energies ( ≈
3. Results
We have taken the results of our FAC calculation, merged where appropriate withother calculations as outlined above, and used the apec code to model the emission froman optically thin plasma with solar photospheric elemental abundances (Anders & Grevesse1989) in collisional ionization equilibrium. We show this result in Figure 2, for T=10 Kplasma with the emission lines broadened by Gaussians with width 0.05˚A. Overplotted onthis figure is the same result from the currently version (2.0) of AtomDB (Foster et al. 2011),which uses the old Fe ix data. Overlaid is the effective area curve of the AIA instrumentwith the 94˚A filter in place, taken from Boerner et al. (2011), which can also be obtainedby the routine aia get response.pro in the SolarSoftware package. It can be seen that thereare clearly two strong lines and several weaker lines, which are also from 5f →
3d transitions,within the region of interest.The weaker lines are a significant fraction of the two main 5f-3d lines, with emissivitiesof around 10-20% of the main lines. Their exact wavelengths are, however, unknown: the5f-3d lines were already weak in the EBIT measurements, the weaker neighboring lines werenot distinguished from the background. The correction applied to the 5f-3d lines was afurther ±
5% compared to the simple multiplication by the 0.9817 scaling factor, in oppositedirections. This implies that a correction at a similar level may be required in the case ofthese weaker lines. We have not further adjusted the energy levels of these weaker linesafter the general initial scaling. Further experimental measurements of these lines would bevaluable in estimating their effects more clearly.In Figure 2 we have also convolved the line emissivities for all ions with the effectivearea of the filter at each wavelength, and show the total as a function of temperature. Wehave done this for the AtomDB 2.0.1 model, which omits the 94˚A lines, and for an identicaldataset but using the new Fe ix data from this work. The low temperature peak, previouslydue to Fe x , is significantly increased due to the strong Fe ix emission as part of this work,by over a factor of 2 at log ( T e /K ) = 5 . ix spectrum. The lines at134.08 and 136.70˚A, identified as belonging to the 3p → transition, are clearlyidentifiable in the new calculations of the spectrum. Figure 3 shows the spectrum calculatedusing the old and new Fe ix data, combined with a quiet Sun spectrum taken from theSDO Extreme Ultraviolet Variability Experiment MEGS. The previously unidentified linesat 134.08˚A and 136.70˚A are clearly observable. These wavelengths fall sufficiently far awayfrom the 131˚A filter transmission band that there is no discernable change in the estimatedflux in this filter due to the inclusion of these lines. 9 – Spectrum at 10 K -
91 92 93 94 95 96 97
Wavelength (Å) E m i ss i v i t y ( - p h c m s - Å - ) old 0.350.300.250.200.150.100.050.00 E ff e c t i v e A r e a ( c m ) newold SDO AIA 94Å Emission vs T E m i ss i v i t y * E ff e c t i v e A r e a ( p h c m s ) - -16 -17 -15 log (T/K)
10 Fe XVIIIFe XFe IX
Fig. 2.—
Left : the emissivity of Fe ix at T = 10 K. Dotted line: from AtomDB v2.0.1; solidline: from AtomDB v2.0.1 with Fe ix data from this work; dashed line: the effective area ofthe 94˚A channel of the SDO/AIA. The AtomDB v2.0.1 data is effectively zero, and hencetoo small to be notable on the graph. Right : The total emissivitiy of elemental emissionlines convolved with the effective area of the 94˚A filter. Dashed line: data from AtomDBv2.0; solid line: data from AtomDB v2.0 including the Fe ix data from this work. 10 –
4. Discussion
The lack of information on the Fe ix emission in the 94˚A region has been well knownsince the work of Lepson et al. (2002). Testa et al (2011) compared the existing atomicdata in chianti ∼ → q , for the low temperature (log ( T /K ) ≤ .
3) responsefunction of the 94˚A filter, R , by fitting their 100 results in the other filters with q afree parameter. They obtained q = 6 . ± . ( T /K ) = 6 . q ≈ ( T /K ) = 5 .
8, and ≈ .
25 at log ( T /K ) = 6 .
0. There is significantdiscrepancy here: it would be an interesting exercise to investigate whether the DEM analysisof Aschwanden & Boerner (2011) can be self consistent using the new emission estimate inthis filter band. It is also possible that there are futher lines from different ions in the filterwhich have not yet been correctly handled.It is difficult to estimate uncertainties in the results from this work due to the manyoverlapping sources of error. As well as the two main lines which are the focus of thiswork, there are many smaller lines of uncertain wavlength. Given the observed and initiallycalculated 5f →
3d wavelengths differ by around 0.5%, adding normally distributed randomerrors to these lines of ± . ix emissionin the 94˚A filter. This 10% fluctuation is then approximately a 5% effect on the totalemission in the band once Fe x is also included. Given that the estimates of uncertainty indistorted wave excitation collisions are usually not better than 20%, this is not expected tobe a dominating source of error in the calculation.For those levels which appear in both this work and the collisional calculation ofStorey, Zeippen & Le Dourneuf (2002), comparison of the collision strengths for excitationfrom the ground state at T = 10 K between this data and our FAC results show that theyvary by on average around 25%. This is a very approximate lower limit on the likely errorson the calculation of emission in the 94˚A band, since excluding cascades from the n=6 shell,this is the only way to populated the 5f upper levels in this model, and for these levels we 11 –are using the distorted wave, not R-matrix, methods.This data has been incorporated into AtomDB, to be released fully in AtomDB v2.1.0which is due for release later in 2011. In the meantime, the data can be obtained from theAtomDB website, .ARF acknowledges funding from NASA ADP grant
REFERENCES
This preprint was prepared with the AAS L A TEX macros v5.2.
13 –
Fe IX lines new old120 125 130 135 140
Wavelength ( ) ( p h c m s ) - - - E m i ss i v i t y SDO EVE quiet sun spectrum F l u x ( W m n m ) - - - Fe IX lines
Fig. 3.—
Top : A quiet Sun spectrum taken from the SDO EVE MEGS instrument.
Bottom :The spectrum calculated using AtomDB 2.0.1, with (dashed) the old Fe ix data and (solid)the new data from this work, with all lines broadened by Gaussians with σ = 0 ..