Table Of Content

Astronomy&Astrophysicsmanuscriptno.o4˙ratios (cid:13)c ESO2009 January22,2009 iv Ultraviolet and extreme-ultraviolet line ratio diagnostics for O F.P.Keenan,P.J.Crockett, K.M.Aggarwal,D.B.JessandM.Mathioudakis AstrophysicsResearchCentre,SchoolofMathematicsandPhysics,Queen’sUniversityBelfast,BelfastBT71NN,NorthernIreland, UK 9 e-mail:[email protected] 0 0 Received;accepted 2 ABSTRACT n a J Aims.We generate theoretical ultraviolet and extreme-ultraviolet emission line ratios for Oiv and show their strong versatility as electrontemperatureanddensitydiagnosticsforastrophysicalplasmas. 5 Methods.RecentfullyrelativisticcalculationsofradiativeratesandelectronimpactexcitationcrosssectionsforOiv,supplemented 1 withearlierdataforA-valuesandprotonexcitationrates,areusedtoderivetheoreticalOivlineintensityratiosforawiderangeof electrontemperaturesanddensities. R] Results.Diagnosticlineratiosinvolvingultravioletorextreme-ultraviolettransitionsinOivarepresented,thatareapplicabletoa widevarietyofastrophysicalplasmasrangingfromlowdensitygaseousnebulaetothedensestsolarandstellarflares.Comparisons S withobservationaldata,whereavailable,showgoodagreementbetweentheoryandexperiment,providingsupportfortheaccuracyof . h thediagnostics.However,diagnosticsarealsopresentedinvolvinglinesthatareblendedinexistingastronomicalspectra,inthehope p thismightencouragefurtherobservationalstudiesathigherspectralresolution. - o Keywords.atomicprocesses–Sun:UVradiation–planetarynebulae:general–ultraviolet:general r t s a 1. Introduction 2. Atomicdataandtheoreticallineratios [ 1 The model ion for Oiv consisted of the 75 fine-structure lev- v els arising from the 2s22p, 2s2p2, 2p3, 2s23ℓ (ℓ = s, p, d), Ultraviolet and extreme-ultraviolet emission lines arising from 2 2s2p3ℓ (ℓ = s, p, d) and 2s24ℓ (ℓ = s, p, d, f) configura- transitionsinB-likeOivaredetectedfromawidevarietyofas- 2 tions.Energiesforalltheselevelswereobtainedfromthecom- 2 tronomicalsources,rangingfromthe Sun (Sandlinet al. 1986) pilation of experimental values by the National Institute of 2 tootherstars(Christianetal.2004),gaseousnebulae(Feibelman Standards and Technology, which may be found at their web- . 1997)andsupernovaremnants(Blairetal.1991).Thediagnos- 1 site http://physics.nist.gov/PhysRefData/. Test calculations in- tic potentialof these lines to provideelectron temperature(T ) 0 e cluding additional levels, such as those arising from the 2s25ℓ and density (N ) diagnostics for the emitting plasma was first 9 e and2s2p4ℓconfigurations,wherefoundtohaveanegligibleef- 0 shown by Flower & Nussbaumer (1975), who also calculated fectonthetheoreticallineratiosconsideredinthepresentpaper. : radiative rates plus electron and proton impact excitation cross v sections for the ion. Since then, many authors have generated EinsteinA-coefficientsfortransitionsin Oiv wereobtained Xi atomicdataforOivthathavesubsequentlybeenusedtoderive from the following sources: (i) Galav´ıs et al. (1998) for the r theoreticaldiagnosticlineratios(seeTayal2006andreferences forbidden 2s22p 2P1/2–2s22p 2P3/2 transition; (ii) Corre´ge´ & a therein). Hibbert (2002) for the 2s22p 2PJ–2s2p2 4PJ′ intercombination lines;(iii)Corre´ge´ &Hibbert(2004)forallowedandintercom- binationlinesamongthe2s22p,2s2p2, 2p3 and2s23ℓ(ℓ = s,p, Very recently, Aggarwal & Keenan (2008) have employed d)levels;(iv)Aggarwal&Keenan(2008)forallremainingtran- the fully relativistic grasp andDirac rmatrx codesto calculate sitions. For electron impact excitation rates, we have adopted radiativeratesandelectronimpactexcitationcrosssections,re- the results of Aggarwal & Keenan, which contain several im- spectively,foralltransitionsamongtheenergeticallylowest75 provementsoverpreviouscalculationsforOivundertakenwith fine-structurelevelsofOiv.Theseresultsarethemostextensive thermatrxcode(Zhangetal.1994;Tayal2006),includingthe currentlyavailableforOiv,andalsoshouldbethemostreliable, greatestnumberoflevelsandthelargestrangeofpartialwaves. at least for the excitation cross sections, as discussed in detail They are hence probably the most accurate currently available byAggarwal&Keenan.Inthispaperweusethesedata,supple- for this ion, as discussed in detail by Aggarwal & Keenan. mentedwith previoushighlyaccuratecalculationsforradiative However, there is also scope for improvement, mainly due to rates and proton excitation cross sections, to derive theoretical the fact that the wavefunctions adopted in the calculations of Oiv ultravioletand extreme-ultravioletemission line ratios ap- Aggarwal&Keenanarenotasaccurateasthoseofsomeother plicable to a wide range of astrophysical plasmas. We demon- workers,suchasTachiev&Froese-Fischer(2000)andCorre´ge´ stratetheversatilityof Oivplasmadiagnostics,whichcanpro- & Hibbert (2002).Indeed, this is why we have adoptedthe A- videtemperatureanddensityestimatesforawidevarietyofas- values of Corre´ge´ & Hibbert (2002, 2004) where possible, as tronomicalsourcesrangingfromlowdensitygaseousnebulaeup their results have an estimated uncertainty of only ±5%, com- tothedensestsolarandstellarflares. pared to ±20% for those of Aggarwal & Keenan. The limita- 2 F.P.Keenan,P.J.Crockett,K.M.Aggarwal,D.B.JessandM.Mathioudakis:LineratiodiagnosticsforOIV tionsinthewavefunctionsofAggarwal&Keenanmaydirectly affectthesubsequentdeterminationofexcitationrates,bothfor allowedandforbiddentransitions.Thisisbecausefortheweak allowed transitions,the A-valuesof Aggarwal& Keenandiffer by up to 50% with those of Tachiev & Froese-Fischer (2000) and Corre´ge´ & Hibbert (2004), while some of the energy lev- elsshowdiscrepanciesofupto8%withtheexperimentalvalues (see Tables 1 and 2 of Aggarwal& Keenan).Nevertheless, the estimated accuracy of the Aggarwal & Keenan excitation rate data is ±20% for a majority of transitions, and should be the mostreliablecurrentlyavailableforOiv. Asnotedby,forexample,Seaton(1964),excitationbypro- tons will be important for the 2s22p 2P –2s22p 2P transi- 1/2 3/2 tion, and in the present analysis we have used the theoretical resultsofFosteretal.(1996).However,Flower&Nussbaumer (1975)havepointedoutthatprotonexcitationshouldalsobein- cluded for the 2s2p2 4P –2s2p2 4P transitions in B-like ions, J J′ andfortheserateswehaveadoptedthecalculationsofFosteret al.(1997).BoththeFosteretal.(1996)andFosteretal.(1997) Fig.1. The I(1407.3Å)/I(1401.1Å) line intensity ratio in Oiv, dataareestimatedtobeaccurateto±10%. where I is in energy units, plotted as a function of logarithmic Using the aboveatomicdata in conjunctionwith a recently electron density (Ne in cm−3) at electron temperatures of Te = updated version of the statistical equilibrium code of Dufton 10000,15000,20000and30000K. (1977), relative Oiv level populationsand hence emission line strengthswere calculatedfortwo gridsof electrontemperature (T ) and density (N ) values. The first grid (for T = 10000, e e e 15000,20000and 30000K; N = 102–106cm−3 in steps of 0.1 e dex) is appropriateto nebular plasmas, while the second (T = e 104.8–105.6K in steps of 0.1 dex; N = 108–1014cm−3 in steps e of 0.1 dex) is for solar/stellar plasma conditions. In particular, the adopted temperature range for the latter covers that over whichOivhasafractionalabundanceinionizationequilibrium ofN(Oiv/N(O)≥0.006(Bryansetal.2008),andhenceshould beappropriatetomostcoronal-typeplasmas.Ourresultsaretoo extensive to reproduce here, as with 75 fine-structure levels in ourcalculationswehaveintensitiesfor2775transitionsateach ofthe530possible(T ,N )combinationsconsidered.However, e e resultsinvolvinganylinepair,ineitherphotonorenergyunits, are freelyavailable fromone ofthe authors(FPK) by emailon request.Givenerrorsintheadoptedatomicdataofbetween±5% and±20%(seeabove),wewouldexpectourtheoreticalratiosto beaccuratetobetterthan±15%. Fig.2.SameasFig.1,butfortheI(1404.7Å)/I(1401.1Å)ratio. 3. Resultsanddiscussion Table1.SummaryofOivtransitions. The Oiv intercombination multiplet around 1400Å provides Wavelength(Å) Transition excellent electron density diagnostics for both nebular and 554.51 2s22p2P –2s2p22P solar plasmas, as shown in Figs. 1–4, where we plot the 3/2 3/2 625.85 2s2p24P –2p34S emission line ratios R = I(1407.3Å)/I(1401.1Å), R = 5/2 3/2 1 2 779.91 2s2p22D –2p32D I(1404.7Å)/I(1401.1Å) and R3 = I(1407.3Å)/I(1404.7Å) as a 787.71 2s22p2P15//22–2s2p22D5/23/2 fliunnecstiaorneolifstTede ainndTaNbel.eT1h,eastraanresittihoonssecfoorrrethspeoontdhienrgOtoivthfeesae- 1739403.2.50 22ss222pp222PP3/2––22ps23p22D2D5/2 3/2 5/2 tures discussed in this paper. We note that the ratios R4 = 1397.2 2s22p2P1/2–2s2p24P3/2 I(1399.7Å)/I(1401.1Å)andR5 =I(1397.2Å)/I(1401.1Å) have 1399.7 2s22p2P1/2–2s2p24P1/2 thesameTe andNe dependenceasR1 andR2,respectively(due 1401.1 2s22p2P3/2–2s2p24P5/2 to common upper levels), but with R4 = 1.02×R1 and R5 = 1404.7 2s22p2P3/2–2s2p24P3/2 0.130×R . 1407.3 2s22p2P3/2–2s2p24P1/2 2 The above theoretical ratios are in good agreement with observations for gaseous nebulae, such as those by Keenan et al. (1993). For example, for the planetary nebula NGC7662, fromlineratiosinspecieswithsimilarionizationpotentialsand Keenan et al. measured R = 0.30, R = 0.69 and R = 0.29, hence spatial distributions to Oiv, such as I(4711Å)/I(4740Å) 1 2 4 implyingelectrondensitiesoflogN =3.5,4.0and3.5,respec- inArivandI(2424Å)/I(2422Å)inNeiv,bothofwhichindicate e tively,fromFigs.1and2.Thesevaluesareconsistent,andalso log N = 3.5 (Keenan et al. 1997, 1998). In addition, we note e in agreementwith the electrondensities derivedfor NGC7662 thatKeenanetal.(2002)havemeasuredOivlineratiosforthe F.P.Keenan,P.J.Crockett,K.M.Aggarwal,D.B.JessandM.Mathioudakis:LineratiodiagnosticsforOIV 3 Fig.3. The I(1407.3Å)/I(1401.1Å) line intensity ratio in Oiv, Fig.5.SameasFig.3,butfortheI(1343.5Å)/I(1407.3Å)ratio. where I is in energy units, plotted as a function of logarithmic electrondensity(N incm−3)attheelectrontemperatureofmax- e imumOivfractionalabundanceinionizationequilibrium,T = e ative to the limb, Feldman & Doschek (1978) measured R = 105.2K(Bryansetal.2008),plus±0.2dexaboutthisvalue. 1 0.20andR =0.19fromSkylab/S082Aspectra,whichbothim- 4 plylogN =10.1fromFig.3,ingoodagreementwiththevalue e oflogN =10.2foundfromlineratiosinNiv,whichisformed e atthesametemperatureasOiv(Keenanetal.1994). The intercombination line ratios in Oiv only provide use- ful electron density diagnostics for values of N up to about e 1012cm−3(seeFigs.3and4).However,Kastner&Bhatia(1984) havepointedoutthattheallowedlinesofOivarisingfrom2s2p2 2P–2p3 2D transitions lie only ∼60Å from the intercombina- tionmultiplet,andtheirintensityratiosareverysensitivetothe electrondensityforN >1011cm−3.Theyhenceshouldprovide e goodN –diagnosticsforveryhighdensityastronomicalplasmas e suchas solar andstellar flares. InFig. 5 we plotthe ratio R = 6 I(1343.5Å)/I(1407.3Å) asa functionofbothT andN , asthe e e 1343.5Åtransitionistheonlylineinthe2s2p22P–2p32Dmul- tiplet which is unblended in existing solar spectra (Cook et al. 1994).ThemeasuredvaluesofR =0.89and0.90fortheflares 6 of 1973 August 9 and 1973 September 7, from Skylab/S082B spectra (Cook et al. 1994), both indicate log N = 12.5 at the e temperature of maximum fractional abundancefor Oiv in ion- Fig.4.SameasFig.3,butfortheI(1407.3Å)/I(1404.7Å)ratio. izationequilibrium,T =105.2K(Bryansetal.2008).Theseare e consistentwiththevaluesoflogN ≃12.3determinedforhigh e densityflaresusingextreme-ultravioletlinesofOv,formedata symbiotic star RRTel. The diagnostic ratios for other species in the RRTel spectrum, ranging from Alii to Ov, indicate log similartemperaturetoOiv(Keenanetal.1991). N ≃ 5–8(see Keenanet al. 2002andreferencestherein),over For temperaturediagnostics, Flower & Nussbaumer (1975) e which density interval the theoretical values of R through R have shown that the intensity ratio of lines within the 2s22p 1 5 arepredictedtobeeffectivelyconstant(seeFigs.1and2).Once 2P–2s2p2 2D multiplet at ∼790Å to those in 2s22p 2P–2s2p2 again,thereisexcellentagreementbetweentheoryandobserva- 2P at ∼554Å allows T to be estimated for the Oiv emitting e tion,withmeasuredandpredictedvaluesof(theoryinbrackets) region of a plasma. This is shown in Fig. 6, where we plot R1 =0.16±0.02(0.18),R2 =0.54±0.05(0.60),R4 =0.17±0.02 the R7 = I(790.20Å)/I(554.51Å) ratio as a function of Te and (0.18)andR5=0.077±0.008(0.077). Ne. Similarly, Curdt et al. (1997) have noted that the R8 = In existing solar spectra, such as those from the HRTS and I(779.91Å)/I(787.71Å)ratioisaT –diagnostic,andthisisplot- e SOHO/SUMER instruments, the Oiv 1404.7Å line is signifi- ted in Fig. 7. An inspection of the two figures reveals that R 7 cantlyblendedwithSiv(Brageetal.1996;Keenanetal.2002), is in principle a better temperature diagnostic than R , as it is 8 although we note that the blending is negligible under nebu- lesssensitivetotheadoptedvalueofN .However,theemission e lar plasma conditions (Keenan et al. 2002). Additionally, the lines in R are much closer in wavelength and hence the ratio 8 1397.2Å feature is very weak in solar spectra, and possibly ismorelikelytobereliablymeasured.Indeed,Curdtetal.have blended,andhenceitsintensityshouldusuallybeconsideredan determinedR =0.033fromaSOHO/SUMERspectrumofthe 8 upperlimit(Brageetal.1996).However,theremaininguseable solar disk, which indicates T ≃ 105.1–105.3K from Fig. 7 (the e density diagnostic line ratios R and R do provide consistent exact value depending on the adopted density), in good agree- 1 4 derivationsofN .Forexample,forActiveRegionBat+2′′ rel- mentwiththetemperatureofmaximumfractionalabundancein e 4 F.P.Keenan,P.J.Crockett,K.M.Aggarwal,D.B.JessandM.Mathioudakis:LineratiodiagnosticsforOIV Fig.6. The I(790.20Å)/I(554.51Å) line intensity ratio in Oiv, Fig.8. Plot of the Oiv line intensity ratio where I is in energy units, plotted as a function of logarithmic I(779.91Å)/I(787.71Å) against I(625.85Å)/I(790.20Å), electrontemperature(Te inK) atlogarithmicelectrondensities whereIisinenergyunits,forlogarithmicelectrontemperatures (Neincm−3)oflogNe =8–13. (TeinK)oflogTe=4.8–5.6,andlogarithmicelectrondensities (N incm−3)oflogN =8–13. e e to be simultaneously determined via ratio – ratio diagrams, as illustratedinFig.8. In summary,we see that ultravioletand extreme-ultraviolet emission lines of Oiv providea diverseportfolioof T andN e e diagnostics,applicabletoawidevarietyofastronomicalsources ranging from gaseous nebulae to high electron density stellar flares.Thepresentlineratiocalculations,whichincludethemost up-to-dateatomicphysicsdata,show goodagreementwith ob- servationswhereavailable,henceprovidingsupportfortheirac- curacy.However,higherspectralresolutionobservationsofsev- eralOiv lines, such as the componentsof the 2s2p2 4P–2p3 4S multipletat∼625Å,wouldbeveryusefultoallowtheirintensi- tiestobereliablymeasuredandemployedasdiagnostics. Acknowledgements. This work has been financed by the Science and TechnologyFacilitiesCouncilandEngineeringandPhysicalSciencesResearch Fig.7.SameasFig.6,butfortheI(779.91Å)/I(787.71Å)ratio. Council of the United Kingdom, while P.J.C. and D.B.J. are grateful to the DepartmentofEducationandLearning(NorthernIreland)fortheawardofstu- dentships. F.P.K.isgrateful toAWEAldermaston fortheaward ofaWilliam PenneyFellowship. ionizationequilibriumforOiv,T =105.2K(Bryansetal.2008). e Unfortunately,toourknowledge,theR ratiohasnotbeenmea- 7 References sured due to the low spectral resolution of existing solar ob- servationsspanningthe554–790Åwavelengthrange.However, Aggarwal,K.M.,&Keenan,F.P.2008,A&A,486,1053 O’Shea et al. (1996) have determined values of the multiplet Blair,W.P.,Long,K.S.,Vancura,O.,etal.1991,ApJ,379,L33 Brage,T.,Judge,P.G.,&Brekke,P.1996,ApJ,464,1030 intensity ratio I(790Å)/I(554Å) for several solar featuresfrom Bryans,P.,Landi,E.,&Savin,D.W.2008,ApJ,submitted spectraobtainedwith theS-055spectrometeronSkylab.These Christian,D.J.,Mathioudakis,M.,Bloomfield,D.S.,Dupuis,J.,&Keenan,F. measurements lie in the range 0.47–0.56, and imply tempera- P.2004,ApJ,612,1140 tureswithin∼0.2dexofthatofmaximumfractionalabundance Cook,J.W.,Keenan,F.P.,&Bhatia,A.K.1994,ApJ,425,861 forOiv. Corre´ge´,G.,&Hibbert,A.2002,J.Phys.B,35,1211 Corre´ge´,G.,&Hibbert,A.2004,ADNDT,86,19 Undersolarplasmaconditions,Oivextreme-ultravioletline Curdt,W.,Feldman,U.,Laming,J.M.,etal.1997,A&AS,126,281 ratios containing a component of the 2s2p2 4P–2p3 4S mul- Dufton,P.L.1977,Comput.Phys.Commun.,13,25 tiplet at ∼625Å are strongly density sensitive (O’Shea et al. Feibelman,W.A.1997,ApJS,112,193 Feldman,U.,&Doschek,G.A.1978,ApJS,37,443 1996).Unfortunately,inexistingsolarspectrathetransitions— Flower,D.R.,&Nussbaumer,H.1975,A&A,45,145 whichlieatwavelengthsof624.62,625.13and625.85Å—are Foster,V.J.,Keenan,F.P.,&Reid,R.H.G.1996,A&A,308,1009 all blended with the strong Mgx resonance line at 624.94Å. Foster,V.J.,Reid,R.H.G.,&KeenanF.P.1997,MNRAS,288,973 However,iftheOivfeaturescouldberesolved,theninconjunc- Galav´ıs,M.E.,Mendoza,C.,&Zeippen,C.J.1998,A&AS,131,499 Kastner,S.O.,&Bhatia,A.K.1984,JQSRT,32,249 tionwithotherrelativelynearbyOivlinestheywouldallowthe Keenan,F.P.,Ahmed,S.,Brage,T.,etal.2002,MNRAS,337,901 temperatureanddensityoftheOivemittingregionofaplasma Keenan,F.P.,Aller,L.H.,Bell,K.L.,etal.1998,MNRAS,295,683 F.P.Keenan,P.J.Crockett,K.M.Aggarwal,D.B.JessandM.Mathioudakis:LineratiodiagnosticsforOIV 5 Keenan,F.P.,Conlon,E.S.,Bowden,D.A.,Feibelman,W.A.,&Pradhan,A. K.1993,ApJS,88,169 Keenan,F.P.,Dufton,P.L.,Harra,L.K.,etal.1991,ApJ,382,349 Keenan,F.P.,Harra,L.K.,Doschek,G.A.,&Cook,J.W.1994,ApJ,432,806 Keenan,F.P.,McKenna,F.C.,Bell,K.L.,etal.1997,ApJ,487,457 O’Shea,E.,Foster,V.J.,Keenan,F.P.,etal.1996,A&A,306,621 Sandlin,G.D.,Bartoe,J.-D.F.,Brueckner,G.E.,Tousey,R.,&VanHoosier,M. E.1986,ApJS,61,801 Seaton,M.J.1964,MNRAS,127,191 Tachiev,G.,&Frose-Fischer,C.2000,J.Phys.B,33,2419 Tayal,S.S.2006,ApJS,166,634 Zhang,H.L.,Graziani,M.,&Pradhan,A.K.1994,A&A,283,319