Problems with Atomic Data: Including All the Lines Robert L. Kurucz

1. Problems with Atomic Data: Including All the Lines Robert L. Kurucz Harvard-Smithsonian Center for Astrophysics 60 Garden Street, Cambridge, MA, USA

2. In 1965 I started collecting and calculating atomic and molecular line data for computing equivalent widths, for synthesizing spectra, and for computing opacities in model atmospheres. I wanted to determine stellar effective temperatures, gravities, and abundances. I still want to. I started using Cowan’s atomic structure programs and managed to get them to work on a CDC 6400 computer.

3. For 23 years I put in more and more lines but I could never get a solar model to look right, to reproduce the observed energy distribution. In 1985 Sugar and Corliss published a compilation of energy levels for the iron group elements. In 1988 I finally produced enough lines, I thought. I completed a calculation of the first 9 ions of the iron group elements.

5. I then tabulated 2 nm resolution opacity distribution functions from the line data for solar abundances. With the ODFs I computed a theoretical model with the solar effective temperature and gravity, the current solar abundances from Anders and Grevesse 1988, mixing-length-to-scale-height ratio l/H = 1.25, and constant microturbulent velocity 1.5 km/s. It generally matched the observed energy distribution from Labs and Neckel. I computed thousands of models for a range of abundances that made observers happy. However, agreement with low resolution observations of integrated properties does not imply correctness.

6. In 1988 the abundances were wrong, the Vturb was wrong, the convection was wrong, and the opacities were wrong because the line lists were incomplete. They are still wrong, but they have improved. In 1988 the Fe abundance was 1.66 times larger than today. There was mixing length convection with an exaggerated, constant Vturb. In the grids of models, the default Vturb was 2 km/s. My 1D models still have mixing-length convection, but now with a depth-dependent Vturb that scales with the convective velocity. 3D models with cellular convection do not have Vturb at all, but use the Doppler shifts from convective motions.

7. Fe II in 1988 Sugar and Corliss (1985) based on Johansson (1978)

8. Inclusion of higher configurations extends the series that merge into continua in the ultraviolet and fills in the visible and infrared. There are higher stages of ionization, heavier elements, and additional molecules that are missing from my current line lists. In 1988 the line lists were incomplete but were balanced by high abundances that made the lines stronger and by high Vturb that made the line cores broader. Now that the abundances are lower and Vturb is lower, I have decided to improve the line lists.

9. New Fe IIfrom Johansson (1978); Sugar and Corliss (1985); Adam, Baschek, Johansson, Nilsson, and Brage (1987); Johansson and Baschek (1988); Rosberg and Johansson (1992); Biemont, Johansson, and Palmeri (1997); Castelli, Johansson, and Hubrig (2008); Castelli, Kurucz, and Hubrig (2009); Castelli and Kurucz (2010) EVEN 46 configurations 19771 levels 421 known levels 2645 Hamiltonian parameters, all CI 48 free LS parameters dev 48 cm-1 d7 d4 4s2 4d d4 4s2 5s d5 4p2 d6 4s d5 4s2 d6 4d d5 4s4d d6 5s d5 4s5s d6 5d d5 4s5d d6 5g d5 4s5g d6 6s d5 4s6s d6 6d d5 4s6d d6 6g d5 4s6g d6 7s d5 4s7s d6 7d d5 4s7d d6 7g d5 4s7g d6 7i d5 4s7i d6 8s d5 4s8s d6 8d d5 4s8d d6 8g d5 4s8g d6 8i d5 4s8i d6 9l d6 9s d5 4s9s d6 9d d5 4s9d d6 9g d5 4s9g d6 9i d5 4s9i d5 4s9l ODD 39 configurations 19652 levels 596 known levels 2996 Hamiltonian parameters, all CI 48 free LS parameters dev 64 cm-1 d6 4p d5 4s4p d6 4f d5 4s4f d4 4s2 4p d4 4s2 5p d4 4s2 4f d6 5p d5 4s5p d6 5f d5 4s5f d6 6p d5 4s6p d6 6f d5 4s6f d6 6h d5 4s6h d6 7p d5 4s7p d6 7f d5 4s7f d6 7h d5 4s7h d6 8p d5 4s8p d6 8f d5 4s8f d6 8h d5 4s8h d6 8k d5 4s8k d6 9p d5 4s9p d6 9f d5 4s9f d6 9h d5 4s9h d6 9k d5 4s9

10. Total E1 lines saved new / old = 7615097 / 1264969 ratio = 6 E1 lines with good wavelengths new / old = 103357 / 45815 ratio = 2.3

11. Fe II forbidden lines even odd total M1 lines saved 207590 3665946 with good wavelengths 38256 66961 between metastable 1232 0 total E2 lines saved 10861275 13550604 with good wavelengths 59008 110668 between metastable 1827 0 Isotopes 54Fe 55Fe 56Fe 57Fe 58Fe 59Fe 60Fe fraction .059 .0 .9172 .021 .0028 .0 .0 Rosberg, Litzen, and Johansson (1993) measured isotopic splitting in 9 lines. All Fe lines must be slightly asymmetric. Hyperfine splitting of 57Fe has not yet been measured in any line.

14. DATA ON KURUCZ WEB SITE FOR EACH COMPLETED ION Least-squares fits to the laboratory energy levels showing all the levels computed. Energy level tables with E, J, identification, strongest eigenvector components, lifetime, A sum, C4, C6, Landé g, with sums complete up to the first energy level not included (n=10). Electric dipole, magnetic dipole, and electric quadrupole linelists. Eigenvalues are replaced by measured energies when data exist. Lines connecting measured levels have correct wavelengths, but most of the lines have predicted, uncertain wavelengths.

15. Lines have radiative, Stark, and van der Waals damping constants, Landé g, and branching fractions. Hyperfine and isotopic splitting are included when lab data exist. Laboratory measurements of gf values and lifetimes. Measured or estimated widths of autoionizing levels. Measured or estimated Shore parameters for Fano profile lines. The partition function for a range of densities.

16. The website tells not only what is known but what is missing. It warns the user that only a small subset of the data we need has been measured. Ultimately the real data must come from the laboratory.

17. NEW LINELISTS ON THE KURUCZ WEB SITE Once the line list for an ion is validated it will be incorporated into the wavelength sorted line lists on my website for computing opacities or detailed spectra. I produced most of my molecular line lists in the 1980s. Recently Bernath, Colin, Ram, etc have made FTS measurements that have yielded better constants and better energy levels and better line positions. I will update my line lists using the new data. I will also add any diatomics and diatomic ions that are missing from my line lists. However, I am concentrating on atomic lines first. When computations or laboratory data with the necessary information are available from other workers, I am happy to use those data instead of repeating the work.

19. H2O with isotopologues Partridge and Schwenke (1997) treated H2O semiempirically. They included H2 16O, H2 17O, H2 18O, and HD 16O. My version has 65,912,356 lines. Barber, Tennyson, Harris, and Tolchenov (2006) massively treated H2 16O. My version has 335,767,086 lines. I used the cutoff gf exp(-hcElo/kT) > 1.e-14 for T=3000K and added in the PS isotopologues. ExoMol

20. Sample recent calculations config levels -------- E1 lines -------- even odd even odd good wl total old total Fe I 61 50 18655 18850 93508 6029023 789176 Fe II 46 39 19771 19652 124654 7834553 1264969 Fe III 49 41 19720 19820 37199 9548787 1604934 Fe IV 61 54 13767 14211 8408 14617228 1776984 Fe V 61 61 6560 7526 11417 7785320 1008385 Fe VI 73 73 2094 2496 3534 9072714 475750 Fe VII 85 86 7132 7032 2326 2816992 90250 Fe VIII 52 52 1365 1244 233 220166 14561 Co I 61 61 10920 13085 15441 3771900 546130 Co II 61 50 18655 19364 23355 10050728 1361114 Co III 44 39 18343 19652 9356 11515139 2198940 Ni I 61 61 4303 5758 9663 732160 149925 Ni II 61 61 10270 11429 55590 3645991 404556 Ni III 61 50 18655 19364 21251 11120833 1309729 Ni IV 44 39 18343 19517 5659 15152636 1918070 Ni V 46 41 10637 19238 10637 15622452 1971819 Ni VI 61 61 13706 15792 12219 17971672 2211919 Ni VII 73 73 24756 19567 3502 28328012 967466 Ni VIII 73 73 12714 8903 758 12308126 602486 Ni IX 85 86 7132 7032 253 2671345 79627 Ni X 52 52 1365 1208 235 285029 0

21. Sample recent calculations config levels -------- E1 lines ------- even odd even odd good wl total old total Sc I 61 61 2014 2318 15546 737992 191253 Sc II 61 61 509 644 3436 116491 49811 Sc III 39 38 134 147 1313 5271 1578 Sc IV 16985 Sc V 49 54 1317 1021 2180 645368 130563 Ti I 61 61 6628 7350 33815 4758992 867399 Ti II 61 61 2096 2318 8188 835027 264867 Ti III 73 68 3636 3845 4090 499739 23742 Ti IV 39 38 134 147 1844 7764 5079 V I 61 61 13767 15952 23342 7043556 1156790 V II 61 61 6740 7422 18389 3932853 925330 V III 61 61 2094 2318 9892 966528 284003 Cr I 47 40 18842 18660 35315 2582957 434773 Cr II 61 61 13767 15890 58996 6970052 1304043 Cr III 61 61 6580 7526 23150 5535931 990951 Mn I 44 39 18343 19652 16798 1481464 327741 Mn II 50 41 19686 19870 31437 4523390 878996 Mn III 61 61 13706 15890 17294 10525088 1589314

22. Sample recent calculations config levels -------- E1 lines ------- even odd even odd good wl total old good P I 32 34 1278 1109 12272 202300 1218 P II 61 61 1616 1638 2954 217038 1095 P III 61 61 668 751 2223 60141 163 S I 61 61 2161 2270 24722 225605 834 S II 34 32 1278 1109 7275 275137 742 S III 191 Cl I 61 61 865 863 17528 256337 3491 Cl II 61 61 1604 1506 9561 258102 1450 Cl III 34 33 1278 1111 949 364878 719 Ar I 52 53 405 396 16649 49824 3553 Ar II 47 47 1001 1024 17188 230953 6982 Ar III 48 48 1682 1790 1881 419776 1008 K I 83 88 1497 1388 2472 49987 732 K II 52 53 405 396 1125 55355 67 K III 47 47 1001 1024 211 313550 232 oldtotal Ca I 61 61 515 612 22782 45753 48573 Ca II 57 56 1497 1388 2433 50436 4227 Ca III 52 53 405 396 2897 58089 11740

23. Sample recent calculations config levels -------- E1 lines ------- even odd even odd good wl total old good F I 1602 F II 1558 F III 3737 Ne I 3955 Ne II 5585 Ne III 439 Na I687912551894445632848 393 NaII 181 NaIII559 Mg I 61 61 272 316 11127 22612 2672 Mg II 44 43 155 169 2832 6018 580 Mg III 34 35 257 260 1839 21805 846 Al I 67 71 936 952 3255 29081 870 Al II 66 58 435 504 4847 31420 3184 Al III 44 43 155 124 2839 5145 369 Si I 61 61 1616 1588 10578 190165 6835 Si II 61 65 892 872 3006 36504 919 Si III 54 50 363 424 2726 25109 1535 Si IV 44 42 155 124 2440 5033 326

24. Sample recent calculations config levels -------- E1 lines ------- even odd even odd good wl total old good H I 1204 He I 1631 He II 469 Li I 568 Li II 142 Be I 53 Be II 234 Be III 29 B I 118 B II 44 B III 131 C I61611500119029931184876 7852 C II 58 54 807 762 4148 26735 979 C III 493 C IV 201 N I 6708 N II 1533 N III 402 O I 1275 O II 2182 O III 1069 O IV 54 58 807 762 5742 58706 550

25. Sample recent calculations config levels -------- E1 lines ------- even odd even odd good wl total old good Cu I 61 61 920 1260 5720 28112 496 Cu II 61 61 4303 5758 14959 622985 4599 Cu III 61 61 10270 11429 17539 5258607 0 Cu IV 55 50 9563 17365 9563 11857712 0 Cu X 85 86 508 3002 159 2910966 0 Zn I 72 72 566 681 6282 34135 135 Zn II 61 61 926 1286 968 31563 6 Zn III 61 61 4303 5758 12674 640536 3053 Sr I 61 61 519 628 22686 42301 74 Y I 61 61 1634 2141 5393 59226 330 Y II 69 65 806 930 7213 145597 186

26. TOTAL: new / old = 260 million / 26 million ratio = 10 REASON: 3 as many levels included now as in 1988 I WILL REPLACE ALL MY PREVIOUS CALCULATIONS AS SOON AS POSSIBLE SO THAT ALL THE DATA WILL BE CURRENT. THEN I WILL EXTEND TO HEAVIER ATOMS AND HIGHER IONS.

29. ATLASES AND SPECTRUM SYNTHESIS High-resolution, high-signal-to-noise spectra are needed to test the line data and the spectrum synthesis programs and to determine the stellar parameters. There are no high quality solar spectra taken above the atmosphere in the ultraviolet, visible, or infrared out to 2.2 microns. There is a recent central intensity atlas produced with an FTS on the ACE satellite (Hase et al. 2010) that covers from 2.2 to 14 microns. In the ultraviolet there are not even “good” quality solar spectra. There are various good quality solar spectra taken through the atmosphere in the visible and infrared. I have been trying to reduce the FTS spectra taken by Jim Brault from Kitt Peak to produce central intensity, limb intensity, flux, and irradiance atlases.

34. H band 1560-1740 nm K band 1920-2100 nm

35. 1x observed 1x telluric solar 10x 10x

36. 1x observed telluric solar 10x

37. My conclusions from working with high quality spectra: Abundances are generally determined from blended features that must be interpreted by synthesizing the spectrum including every significant blending line. In general, one half the lines are missing from the list of lines with good wavelengths. Every line has to be adjusted in wavelength, damping constants, and gf value, and most are asymmetric from hyperfine and isotopic splitting. There are pressure shifts. There are depth-dependent Doppler shifts from motions. Most lines used in abundance analyses are not suitable. Including many lines reduces the accuracy. We do not know anything with certainty about the sun except its mass.

38. Conclusions Inclusion of higher energy levels, higher stages of ionization, heavier elements, and additional molecules will increase the opacity in stellar atmosphere, pulsation, stellar interior, asteroseismology, nova, supernova, and other radiation hydrodynamic calculations. Detailed and more complete linelists will allow more accurate interpretation of features in spectra, and the more accurate determination of stellar properties, at any level from elementary 1D approximations to the most sophisticated 3D time-dependent treatments.

40. Using HR6000 as a laboratory light source for Fe II Chemically peculiar or CP stars are early type stars with large over- and underabundances. They can have very small projected rotation velocities, hence narrow lines. HR6000 has Teff 13450K , log g=4.3, and projected rotation velocity about 1.5 km/s from Castelli and Hubrig (2007). The abundances (log relative to solar) are Fe [+0.9], Xe [+4.6], P [>+1.5], Ti [+0.55], Cr [+0.2], Mn [+1.5], Y [+1.2], Hg [+2.7], and He, C, N, O, Al, Mg, Si, S, Cl, Sc, V, Co, Ni, and Sr underabundant.

41. With initial guidance from Johansson, Castelli analyzed the Fe II lines and has determined 126 new 4d, 5d, 6d, and 4f energy levels. These levels produce more than 18000 lines throughout the spectrum from ultraviolet to infrared. Castelli, Johansson, and Hubrig (2008) Castelli, Kurucz, and Hubrig (2009) Castelli and Kurucz (2010) Hubrig is obtaining infrared spectra to extend this work. These lines appear in more “normal” stars as well but are smeared out and blended by rotation velocities 10 to 100 times higher.

42. Computed Fe II spectrum for HR6000 2008 Castelli and Kurucz 2010

43. Computed spectrum for HR6000

44. In stars these Fe II lines are seen in absorption. The Boltzmann factor for the lower level determines the line strength. Lab sources in emission have to populate the upper level. It would make sense to use a large amount of telescope time to make high-resolution, high-signal-to-noise atlases in the UV, visible, and IR of selected CP stars so that as many elements as possible can be analyzed to higher energies than are feasible in the lab.

45. kurucz.harvard.edu/atoms … …