Oxygen spectral line synthesis: 3D non-LTE with CO5BOLD hydrodynamical model atmospheres
D. Prakapavicius, M. Steffen, A. Kucinskas, H.-G. Ludwig, B. Freytag, E.Caffau, R.Cayrel
aa r X i v : . [ a s t r o - ph . S R ] M a r Mem. S.A.It. Vol. 75, 282 c (cid:13) SAIt 2008
Memorie della
Oxygen spectral line synthesis: 3D non-LTE with CO BOLD hydrodynamical model atmospheres
D. Prakapaviˇcius , M. Ste ff en , , A. Kuˇcinskas , , H.-G. Ludwig , B. Freytag ,E. Ca ff au , , R. Cayrel Vilnius University Institute of Theoretical Physics and Astronomy, A. Goˇstauto 12,Vilnius LT-01108, Lithuania Leibniz-Institut f¨ur Astrophysik Potsdam, An der Sternwarte 16, D-14482, Potsdam,Germany Vilnius University Astronomical Observatory, M. K. ˇCiurlionio 29, Vilnius LT-03100,Lithuania ZAH Landessternwarte K¨onigstuhl, D-69117 Heidelberg, Germany Centre de Recherche Astrophysique de Lyon, UMR 5574, CNRS, Universit´e de Lyon,´Ecole Normale Sup´erieure de Lyon, 46 All´ee d’Italie, F-69364 Lyon Cedex 07, France GEPI, Observatoire de Paris, CNRS, UMR 8111, 61 Av. de l’Observatoire, 75014 Paris,France
Abstract.
In this work we present first results of our current project aimed at combiningthe 3D hydrodynamical stellar atmosphere approach with non-LTE (NLTE) spectral linesynthesis for a number of key chemical species. We carried out a full 3D-NLTE spectrumsynthesis of the oxygen IR 777 nm triplet, using a modified and improved version of ourNLTE3D package to calculate departure coe ffi cients for the atomic levels of oxygen in a CO BOLD
3D hydrodynamical solar model atmosphere. Spectral line synthesis was subse-quently performed with the
Linfor3D code. In agreement with previous studies, we findthat the lines of the oxygen triplet produce deeper cores under NLTE conditions, due to thediminished line source function in the line forming region. This means that the solar oxygenIR 777 nm lines should be stronger in NLTE, leading to negative 3D NLTE–LTE abundancecorrections. Qualitatively this result would support previous claims for a relatively low solaroxygen abundance. Finally, we outline several further steps that need to be taken in order toimprove the physical realism and numerical accuracy of our current 3D-NLTE calculations.
1. Introduction
Photospheric abundances of chemical elementsderived from stellar spectra are importantmeans for testing and constraining models ofthe formation and evolution of the Galaxy andits various stellar populations. The reliabilityof the derived chemical abundances is limited,apart from the quality of the observational data, by the realism of the ingredients used in theabundance analysis: atomic data that describethe spectral lines themselves, stellar model at-mospheres, and the allowance of possible de-partures from local thermodynamic equilib-rium (LTE).During the recent years, reliable spec-tral line data has been measured and / or com-puted for a large number of astrophysically rakapaviˇcius et al.: Oxygen spectral line synthesis in 3D-NLTE 283 relevant spectral lines, and departures fromLTE are currently accounted for with an in-creasingly more realistic treatment of colli-sional processes. However, the stellar modelatmospheres that are commonly used for theabundance analysis are based on a numberof critical simplifications: they are typicallyconstructed in one-dimensional (1D) geome-try - plane-parallel or spherically-symmetric -and are subject to hydrostatic and radiative-convective equilibrium (see, e.g., Castelli& Kurucz 2004; Brott & Hauschildt 2005;Gustafsson et al. 2008). Even though the inputmicrophysics (opacities, equation of state) ofthese models is su ffi ciently realistic, the con-vective energy transport, one of the main pro-cesses shaping the physical structure of thephotosphere, is treated in the approximationof the mixing-length theory (B¨ohm-Vitense1958) or its derivatives (Canuto & Mazzitelli1991).In this respect, three-dimensional (3D) hy-drodynamical stellar model atmospheres aremuch more realistic, as they are able to accountfor convection based on first principles with-out the need of free parameters (see Nordlund1982; Stein & Nordlund 1998; Asplund et al.2000; Freytag et al. 2002; Wedemeyer et al.2004). Moreover, this type of model atmo-spheres naturally allows for the emergence ofa surface granulation pattern, horizontal inho-mogeneities and wave activity, all being uniqueproperties of 3D hydrodynamical model atmo-spheres. It has been found that the interplayof these physical processes significantly altersspectral line formation, which may lead to sub-stantial di ff erences in the abundances derivedwith 3D and 1D model atmospheres, respec-tively (Collet et al. 2007; Dobrovolskas et al.2010; Ivanauskas et al. 2010; Kuˇcinskas et al.2013; Dobrovolskas et al. 2013). These find-ings conspicuously indicate that the 3D pho-tospheric structure and dynamics has a signifi-cant impact on the spectral line formation, andshould be properly taken into account in thechemical abundance analysis.Besides the application of realistic stel-lar model atmospheres, an adequate treatmentof non-LTE (NLTE) processes can be alsovery important for deriving reliable chemi- cal abundances. In the optically thin line-forming regions, the absorbing particles ex-perience a radiation field that is of non-localorigin since it forms deeper in the photo-sphere. Consequently, radiation field in theline-forming region may exhibit significantdeviations from the local Planck function.Radiation of non-local origin can distort thecollisional ionization balance given by theSaha equation, and drive the population num-bers of the upper and lower atomic levels ofthe given transition away from the Boltzmanndistribution that is valid in LTE (for a thoroughdiscussion of these e ff ects see, e.g. Bruls et al.1992). Departures from LTE modify both thestrength and shape of the spectral lines, andtherefore can significantly alter spectroscopi-cally derived chemical abundances, in particu-lar at low metallicities (e.g., Th´evenin & Idiart1999).Given the significance of NLTE e ff ects andthe magnitude of the LTE 3D-1D abundancecorrections (especially in the metal-poor stars),it is obvious that the two factors should be si-multaneously taken into account in order toderive reliable abundance estimates. However,the joint 3D-NLTE approach has only been ap-plied in a few selected cases so far (Asplundet al. 2004; Shchukina et al. 2005; Cayrel et al.2007; Pereira et al. 2009; Sbordone et al. 2010;Ste ff en et al. 2012), therefore a systematic ap-plication of this admittedly very demandingmethodology to, e.g., the investigation of stel-lar populations, is yet to come.Driven by the need to combine modern 3Dstellar model atmospheres and non-LTE spec-tral line synthesis, we have recently started aproject to make this methodology available fora wider range of chemical elements to be stud-ied with 3D hydrodynamical CO BOLD stellarmodel atmospheres. Oxygen is a particularlyinteresting element to investigate using the full3D NLTE approach: it is the most abundantchemical element besides hydrogen and he-lium, and its photospheric abundance is widelyused to trace the formation and chemical evolu-tion of various Galactic populations. It is wellknown that the O i IR triplet ( λ =
777 nm) ex-periences significant departures from the LTE(Kiselman 1993; Fabbian et al. 2009, and ref-
84 Prakapaviˇcius et al.: Oxygen spectral line synthesis in 3D-NLTE erences therein). Due to its high ionizationpotential, oxygen does not experience signif-icant overionization in late-type stars, so thatNLTE e ff ects are mainly limited to deviationsfrom the thermal excitation equilibrium. Thesephysical aspects limit the range of possibleNLTE e ff ects in the case of oxygen and there-fore make it a good test case for the full 3D-NLTE approach with CO BOLD model atmo-spheres.
2. Methodology
The 3D hydrodynamical solar model atmo-sphere used in this work was computed withthe CO BOLD code (Freytag et al. 2012). The CO BOLD code solves time-dependent equa-tions of compressible hydrodynamics and ra-diation transfer on a 3D Cartesian grid.Computed in the ”box-in-a-star” setup (fordetails see, e.g., Freytag et al. 2012), oursolar model atmosphere was allowed toevolve hydrodynamically for several convec-tive turnover times (see Ludwig & Kuˇcinskas2012, Appendix A, for a definition of di ff erenttime scales). This particular CO BOLD simula-tion was also used in the studies of Ca ff au etal. (2008) and Beeck et al. (2012), to which werefer the reader for a more detailed descriptionof the input microphysics and physical proper-ties of the model itself.A representative sub-sample of twenty 3Dmodel snapshots (i.e. model structures calcu-lated at di ff erent instants in time) was cho-sen out of the relaxed part of the 3D modelrun in order to produce a statistically repre-sentative and uncorrelated snapshot selection.More specifically, snapshots in this sub-samplewere chosen in such a way that the averageemerging radiation flux and its standard devi-ation would match the corresponding valuesof the entire 3D model run. Similar require-ments were applied in the case of the horizon-tally averaged vertical mass flux at characteris-tic optical depths. The final selection of the 3Dmodel snapshots obtained according to thesecriteria was subsequently used in the evalua-tion of NLTE e ff ects (Sect. 2.2) and, later, in the spectral synthesis calculations of the O i IRtriplet (Sect. 2.3).The original model snapshots had 140 gridpoints in each horizontal direction and 150 gridpoints on the vertical axis, corresponding toa spatial coverage of 5 . × . × .
27 Mm.The vertical grid of the model spanned the op-tical depth range of − . < log τ Ross < . ffi cient to cover the depths wherethe O i IR triplet lines form. For the calcula-tion of departure coe ffi cients and spectral linesynthesis, a coarser 3D model atmosphere wasconstructed by choosing every third grid pointhorizontally, thereby reducing horizontal res-olution of the model to 47 ×
47 grid points.We have verified that di ff erences in the spec-tral synthesis results obtained with the full andreduced model atmospheres, respectively, werenegligible. Departures from LTE in the line forma-tion computations are quantified via three-dimensional sets of departure coe ffi cients which in our study were computed with theNLTE3D code (see Cayrel et al. 2007; Ste ff enet al. 2012). We have recently made numer-ous improvements and generalizations to thecode in order to adapt it for a wider varietyof model atoms and astrophysical tasks. Morespecifically, we included IONDIS / OPALAMroutines, originally part of the Kiel stellaratmosphere package. These routines providepartition functions for a variety of chemicalspecies and are also used for the computa-tion of LTE population numbers and contin-uous opacities at the wavelengths of the linetransitions in a given model atom. Since theseroutines are also used in the spectrum synthe-sis code
Linfor3D (Sect. 2.3), this also con-tributes towards the self-consistency betweenthe NLTE3D and
Linfor3D packages.During the first step, the NLTE3D codecomputes photo-ionization and collisionalrates, where the upward and downward col- The departure coe ffi cient for atomic level i = . . . i max is defined as b i = N i , NLTE / N i , LTE , where N i is the level population for the respective case.rakapaviˇcius et al.: Oxygen spectral line synthesis in 3D-NLTE 285 lisional rates are treated in detailed balanceand, hence, only the upward rates need tobe computed explicitly. These rates are keptconstant throughout all further computations.After this step, radiation transfer calculationsare done for each of the considered line transi-tions, ℓ = . . . ℓ max , to compute the mean lineintensity J ℓ ( x , y , z ) at all grid points, where J refers to the angle-averaged intensity, and over-bar indicates averaging over the line profile.Typically, we use 16 inclined plus the verti-cal direction for angular averaging, and 37 fre-quencies to resolve the line profile. Then, thephoto-excitation rates are computed using J ℓ ,and all rates at each grid point of the 3D modelsnapshot are passed to the statistical equilib-rium routines that compute NLTE populationdensities according to the prescriptions givenin Mihalas (1970). Given J ℓ , a set of linearequations needs to be solved for the unknowndeparture coe ffi cients b i , i = . . . i max , whichis done using standard linear algebra routines,independently for each 3D model grid cell.Once the new iteration of NLTE populationnumbers is completed, the NLTE line opaci-ties are updated and the next iteration is startedto compute line radiation transfer in order toobtain updated photo excitation rates. This cy-cle is repeated via the ordinary Λ -iterationscheme until the relative change in the selectedNLTE line equivalent widths (EWs) becomesless than 10 − per iteration (see also Sect. 3.2). The Grotrian diagram of the oxygen modelatom used in our study is shown in Fig. 1. Themodel atom consists of i max =
16 levels, con-nected by 16 bound-free and ℓ max =
31 bound-bound transitions. Atomic data that describethe levels (energies, statistical weights) and ra-diative transitions (Einstein coe ffi cients) weretaken from the NIST database. Photoionizationcross-sections for the radiative bound-freetransitions were adopted from the Topbase ofthe Opacity Project (Cunto et al. 1993, and fur-ther updates).Excitation and ionization due to collisionswith neutral hydrogen atoms was treated via S D D S P D F G S P D F G [OI] OI IR triplet E ne r g y ( e V ) Fig. 1.
Oxygen model atom used in this work.Radiatively allowed transitions are marked bysolid (green) lines, while radiatively forbiddentransitions that were treated only via electron-impact excitation are marked by dashed (blue)lines. The forbidden [O i ] line and the O i IRtriplet are marked by dash-dotted (red) lines.Collisional and radiative bound-free transitionswere taken into account for each level.the Drawin (1969) formula in the formulationof Lambert (1993). In the present work, we set S H , a parameter that scales the hydrogen col-lision rates, to 1.0. Collisional ionization byelectrons was treated using the classical pre-scription of Seaton (1962). Rate coe ffi cientsfor the excitation by inelastic electron colli-sions were taken from the work of Barklem(2007), allowing us to include the collisionaltransitions between the triplet and quintet sys-tems. Finally, we include a resonant chargetransfer reaction O + H + ⇋ O + + H forthe ground level of oxygen, in the prescrip-tion by Arnaud & Rothenflug (1985). The latterprocess is very e ffi cient in late-type stars andtherefore ensures that the ground level of O ii is in LTE with respect to the ground level ofO i .
86 Prakapaviˇcius et al.: Oxygen spectral line synthesis in 3D-NLTE
For the computation of the photo-ionizingradiation flux, opacity distribution functionsfrom Castelli & Kurucz (2004) were used,while the continuous opacity was calcu-lated with the IONDIS / OPALAM routines.Background opacities stemming from thebound-bound transitions of elements other thanoxygen are not yet included in the current ver-sion of the NLTE3D code. Tests have shown,however, that they are not important in the caseof the oxygen model atom used in this study.In the statistical equilibrium calculations,we treated the O i ground level (2p P) and theupper level of the O i IR triplet (3p P) as sin-glets, while, when performing spectrum syn-thesis calculations, we have taken the fine-splitting into account, assuming that the depar-ture coe ffi cients are identical for all sub-levels:due to their close energetic values, they shouldbe e ffi ciently thermalized and thus experienceidentical sensitivity to NLTE e ff ects. Spectral synthesis calculations of the O i IR triplet lines were done with
Linfor3D .Firstly, Linfor3D calculates the LTE linesource function, S LTE ( ν ) = B ν (Planck’s blackbody function) and line opacity, κ LTE ( ν ) forany given line transition. Whenever NLTEspectrum synthesis is requested, both the linesource function and the line opacity are modi-fied according to: S NLTE ( ν ) S LTE ( ν ) = exp( h ν kT ) − b low / b up ) exp( h ν kT ) − , (1)and κ NLTE ( ν ) κ LTE ( ν ) = b low exp( h ν kT ) − ( b up / b low )exp( h ν kT ) − , (2)where b low and b up are the departure coef-ficients of the lower and upper level of thetransition, respectively. Once the line sourcefunction and line opacity are computed ei-ther in LTE or NLTE, the radiation transferis calculated along 16 inclined plus the ver-tical direction, taking into account the di ff er-ential Doppler shifts along each line-of sight. http: // / ∼ mst / Linfor3D / linfor.pdf This procedure is repeated for every of thetwenty 3D model snapshots. Finally, the result-ing spectral lines synthesized along each of thedi ff erent directions are combined into a singlespectral line profile by spatial, temporal, andangular averaging.
3. Results i IR triplet spectra
We have conducted NLTE and LTE spectrumsynthesis calculations of the O i IR triplet linesusing a 3D solar model atmosphere computedwith the CO BOLD code. Fig. 2 shows the ob-tained synthetic NLTE and LTE O i IR tripletspectrum (identical oxygen abundances wereused in the LTE and NLTE computations).It can be immediately seen that both shapeand strength of the O i IR triplet lines is sen-sitive to NLTE e ff ects: while the line wingsare very similar in both cases, deeper linecore is present in NLTE. Hence, in accordancewith the previous studies, NLTE e ff ects lead tohigher equivalent widths of the O i IR tripletlines and to negative 3D NLTE–LTE abun-dance corrections. Such behavior is qualita-tively very similar to that reported by Asplundet al. (2004) or Pereira et al. (2009), which wasfound to be one of the major factors leading toa lower solar oxygen abundance.The nature of the NLTE spectral line for-mation can be investigated by examining thedependence of NLTE e ff ects on the continuumintensity across the stellar surface, where highand low continuum intensity represents gran-ular and intergranular regions, respectively.Fig. 3 shows the distribution of the NLTE toLTE ratios of local EWs computed from thevertical ray (disk-center intensity) and plot-ted versus the local relative continuum inten-sity. While the plot reveals significant di ff er-ences with respect to the results obtained byAsplund et al. (2004, Fig. 4), who found di-minished NLTE EWs in some (tough not all)intergranular lanes, our results show a quitegood qualitative agreement with the computa-tions of Kiselman (1993, Fig. 8) (note, how-ever, that the adopted S H values were di ff er-ent in all three investigations). Our results indi- rakapaviˇcius et al.: Oxygen spectral line synthesis in 3D-NLTE 287 R e l a t i v e f l u x Wavelength (nm)
Fig. 2.
Synthetic 3D NLTE (black line) and 3D LTE (red dots) O i IR triplet lines in the solar spec-trum calculated with identical oxygen abundance (disk-integrated flux spectrum). Spectral linesynthesis calculations were done using twenty 3D model snapshots of a solar model atmospherecomputed with the CO BOLD code.cate that, in NLTE, line strengths are enhancedat every position on the disk and NLTE ef-fects are more pronounced in the intergranularregions (low continuum intensity). Kiselman(1993) suggested that this happens because inthe intergranular regions the triplet lines formhigher in the atmosphere where the departuresfrom LTE are more severe.The origin of the NLTE e ff ects can beexamined by comparing NLTE and LTE linesource functions and line opacities (see, e.g.,the analysis of Kiselman 1993). Fig. 4 showsthe ratio of NLTE and LTE line source func-tions (top panel) and line opacities (bottompanel) for the 777.19 nm component of theO i IR triplet, as given by Equations (1) and(2). As was stated previously, the 3p P sub-levels share identical departure coe ffi cients, sothe factor b low / b up that enters the equations andhence the ratios S NLTE / S LTE and κ NLTE /κ LTE are identical for each component of the triplet. The plot shows that the source functiondecreases below the local Planck function atlog τ Ross . .
0. Fig. 4 also contains two spa-tially and temporally averaged flux contribu-tion functions for the line depression (seeMagain 1986) that were computed at the linecenter (777.1954 nm) and wing (777.15 nm)of the line profile. It can be seen that the linewings form in a region where S NLTE is iden-tical or very similar to B ν , while the line coreforms where significant departures from LTEmay occur.On the other hand, the line opacity of theO i IR triplet stays close to LTE in the entireline forming region. The NLTE / LTE ratio ofline opacities depends mostly on b low , whichis close to unity in the entire optical depthrange where the O i IR triplet lines form, whilethe sensitivity to b low / b up ratio is rather small.Hence, the influence of NLTE e ff ects on theline opacity is weak, and therefore it can beinferred that the strengthening of the O i IR
88 Prakapaviˇcius et al.: Oxygen spectral line synthesis in 3D-NLTE
OI 7772
Normalized continuum intensity E W N L T E / E W L T E Fig. 3.
Probability density plot showing theNLTE to LTE equivalent width ratio of the777 .
19 nm component of the O I IR triplet,plotted against the normalized local continuumintensity for all twenty 3D model snapshotsthat were used in the calculations. Both con-tinuum intensity and equivalent width refer tothe disk-center solar spectrum (vertical rays).triplet happens solely due to the diminishedline source function. According to Fabbian etal. (2009, and references therein), this is causedby the photon losses in the line.
Fig. 5 shows the evolution of the equivalentwidth of the 777 .
19 nm line (top panel) andthe relative change of EW (bottom panel) as afunction of the iteration number. As stated pre-viously, the Λ -iterations are continued until therelative change in all NLTE equivalent widthsof the selected radiative transitions (green linesin Fig. 1) becomes less than 10 − per iteration.Even though the triplet line shown in Fig. 5satisfies the convergence criterion already af-ter a small number of iterations, certain otherlines (mainly the resonant UV lines, not shownin the figure) may show much slower conver-gence and may thus require significantly moreiterations to obtain the final NLTE populationdensities. -0.20.00.20.4 l og ( S N L T E B ) -0.50.00.51.0 OI 7772 -4 -3 -2 -1 0 1-0.20.00.20.4 N o r m a li z ed c on t r i bu t i on f un c t i on log Ross l og ( N L T E L T E ) -0.50.00.51.0 Flux contribution functions: line depression at core line depression at wing
Fig. 4.
NLTE-to-LTE ratio of the line sourcefunction (top panel) and line opacity (bottompanel) plotted versus Rosseland optical depth(gray scales represent the probability density).Both panels contain the same normalized fluxcontribution functions for the line depressionat the core (777 . .
15 nm, dot-dashed) of the O i ∼
30 or as large as ∼ i IRtriplet lines continue to grow even after ∼ Λ -iteration scheme pose a well-known prob-lem in radiation transfer calculations. To quoteHubeny (2003): “it exhibits a pathological be-havior in that the solution stabilizes (i.e. rel-ative changes of the source function becomeextremely small) long before the correct so-lution is reached”. All this indicates that amore e ffi cient iteration scheme needs to be im-plemented into the NLTE3D code in order tomake the computations more e ffi cient and ac-curate. rakapaviˇcius et al.: Oxygen spectral line synthesis in 3D-NLTE 289 E W N L T E / E W L T E OI 7772 E W / E W Iteration number
Fig. 5.
Top panel: evolution of the disk-integrated equivalent width (EW) of the O i i triplet component. The figureshows the iteration progress in five individual3D model snapshots. Note that in the bottompanel data from the individual snapshots mergeinto one single curve.
4. Conclusions
We provide a short summary of our first resultsregarding the 3D NLTE spectrum synthesis ofthe O i IR triplet lines, carried out using a 3Dhydrodynamical solar model atmosphere com-puted with the CO BOLD code. Atomic levelpopulation numbers were calculated using asignificantly expanded and improved versionof the NLTE3D code. Our results show that,in agreement with previous studies, the O i IR triplet lines are sensitive to NLTE e ff ects,which lead to deeper line cores than those ex-pected in LTE. This happens mainly becausein the range of optical depths where the coresof the O i IR triplet lines form the line sourcefunction becomes smaller than the local Planckfunction. A significant deepening of the core,along with a net strengthening of the equivalent width of the line, leads to negative 3D NLTE–LTE abundance corrections.The current version of the NLTE3D codeutilizes an ordinary Λ -iteration scheme for thesolution of non-linear statistical equilibriumequations. Such approach may be adequate incases where all line transitions are weak andthus the radiative rates in the lines are onlyweakly coupled to the level populations (e.g.lithium). This, however, is obviously not truein the case of oxygen. For a proper treatment ofthis more general situation, the implementationof a faster and more reliable iteration schemevia some form of accelerated Λ -iteration (e.g.Olson et al. 1986; Rybicki & Hummer 1991)may be needed. This will be amongst the mainpriorities for the further development of theNLTE3D code, in order to ensure a higher re-liability of the numerical results and a betterversatility of the code in further applicationsinvolving more complicated model atoms. Acknowledgements.
This work was supported bygrant from the Research Council of LithuaniaMIP-101 / References
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