Nitrogen Abundances in Early-Type Be Stars

293 Pages·2017·7.15 MB·English

by  Ahmed Ahmed

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Electronic Thesis and Dissertation Repository
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NNiittrrooggeenn AAbbuunnddaanncceess iinn EEaarrllyy--TTyyppee BBee SSttaarrss
Ahmed Ahmed, The University of Western Ontario
Supervisor: Dr. T.A.A. Sigut, The University of Western Ontario
A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree
in Astronomy
© Ahmed Ahmed 2015
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NITROGEN ABUNDANCES IN EARLY-TYPE BE STARS
(Thesis format: Monograph)
by
Ahmed Ahmed
Graduate Program in Astronomy
A thesis submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
The School of Graduate and Postdoctoral Studies
The University of Western Ontario
London, Ontario, Canada
(cid:13)c Ahmed M. H. Ahmed 2015
Abstract
A sample of 26 Be stars from the Magnetism in Massive Stars (MiMeS) spectroscopic
surveyareanalyzedfortheirphotosphericnitrogenabundancesinanefforttodetectrotational
mixing in the Be stars. Be stars are massive stars, between 3 and 20 times the mass of the
Sun, that are surrounded by a thin, equatorial disk of gas that produces emission lines in their
optical and near-infrared spectra. Be stars are the most rapidly-rotating stellar population on
the main sequence, where stars produce energy by core hydrogen burning. New, non-LTE
line transfer calculations are performed for the Nii ion, the dominant ionization stage in the
photospheres of the B stars, and an extensive error analysis is performed via Monte Carlo
simulation to determine the achievable accuracy of nitrogen abundances among these stars.
To analyze the measured Nii equivalent widths from the MiMeS survey, the effects of both
gravitational darkening, due to the rapid rotation of the central B star, and the veiling effect of
emission from the Be star circumstellar disk are considered. Both of these effects are found
to be small for the sample population, affecting the final nitrogen abundances at the level ≈
±0.1 dex. The final, average nitrogen abundance for the MiMeS sample, AMiMeS = 7.78,
N
hasavalueingoodagreementwiththesolarabundance, A◦ = 7.83,andrecent,high-precision
N
abundancemeasurementsformainsequenceBstars. Nevertheless,theMiMeSsamplestandard
deviation is over a factor of two larger than that of the observed nitrogen abundances in the
atmospheres of B stars in the solar neighbourhood, with many low abundance objects and a
few high abundance objects. No discernible trend of the nitrogen abundance can be seen with
stellar gravity, logg (as a proxy for stellar age), or stellar equatorial velocity in the MiMeS
survey. It is suggested that possible disk emission in the Nii line transitions may explain the
lowerabundanceobjects,andthiswillbethesubjectoffuturework.
Keywords: stars: abundances-stars: atmospheres-stars: rotation-radiativetransfer-line:
formation
ii
Acknowlegements
IwouldtolikeexpressmysinceregratitudetomysupervisorAaronSigutforhisexpertiseand
patience. Also,IwouldliketothankmyadvisorycommitteemembersMartinHoudeandJohn
D. Landstreet for their continuous support and suggestions. Finally, I would like to thank my
examiners for their helpful comments and suggestions, Drs Gregg Wade, Jan Cami, John D.
Landstreet,andPaulRagogna.
iii
Contents
Abstract ii
Acknowlegements iii
ListofFigures vii
ListofTables xii
ListofAppendices xv
1 IntroductionandOverview 1
2 Early-TypeStars 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 PhysicalCharacteristicsofMassiveStars . . . . . . . . . . . . . . . . . . . . . 6
2.3 SurfaceAbundancesofB-typestars . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 EvolutionofMassiveStarsonTheMainSequence . . . . . . . . . . . . . . . 9
2.4.1 EffectsofRotationonMassiveStarEvolution ontheMain-Sequence . . 11
RotationalMixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
ModellingResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.2 ObservationalConstraintsonRotationalMixinginMassivestars . . . . 22
3 TheClassicalBestars 28
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 SpectralfeaturesofBeStars . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 PossibleFormation MechanismsofBeStarDisks . . . . . . . . . . . . . . . . 33
3.4 Diskstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 BeStarsandRotational Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4 TheNon-LTERadiativeTransferProblem 37
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 TheRadiativeTransferEquation . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.1 LocalThermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . 41
4.2.2 non-LocalThermodynamic Equilibrium . . . . . . . . . . . . . . . . . 42
4.2.3 NumericalSolutionofTheNon-LTERadiativeTransferProblem . . . . 42
5 Non-LTEforCalculation N ii 45
iv
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 PreviousWorks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.3 NitrogenAtomicData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.3.1 Nii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.3.2 Niii andNiv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.4 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.4.1 IonizationBalancesandDepartureCoefficients . . . . . . . . . . . . . 57
5.4.2 EquivalentWidths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.5 Multi-multi Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.6 TheAccuracyofthePredictednon-LTEEquivalentWidths . . . . . . . . . . . 77
5.6.1 RandomErrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.6.2 SystematicErrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6 Non-LTECalculation forHe i 87
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2 Previousworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3 HeiAtomic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.4 CalculationGridofHeiAtom . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.4.1 IonizationBalancesandDepartureCoefficients . . . . . . . . . . . . . 97
6.4.2 EquivalentWidths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.5 TheAccuracyofthePredictednon-LTEEquivalentWidths . . . . . . . . . . . 106
7 Gravitational Darkening 108
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.2 Gravitational DarkeningAssumingSolidBodyRotation . . . . . . . . . . . . . 108
7.3 Gravitational DarkeningEffectsonSpectralLines . . . . . . . . . . . . . . . . 113
7.3.1 Gravitational DarkeningEffectsonNiiλ3995Å . . . . . . . . . . . . . 114
7.3.2 Gravitational DarkeningeffectsonHeiλ6678Å . . . . . . . . . . . . 117
7.3.3 Gravitational DarkeningeffectsonMgiiλ4481Å . . . . . . . . . . . . 118
7.3.4 Gravitational DarkeningEffectsonv siniMeasurements . . . . . . . . 119
8 NitrogenAbundancesforaSampleofBeStarsfromtheMiMeSSurvey 122
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.2 TheBestarSample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.2.1 SpectraNormalization . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.2.2 StellarParameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8.2.3 EquivalentWidthMeasurements . . . . . . . . . . . . . . . . . . . . . 146
8.3 EstimationsofDiskParameters . . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.4 NitrogenAbundances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.4.1 Estimations of Nitrogen Abundances Based Solely on the Observed
EquivalentWidths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.4.2 Corrections for Circumstellar Disks Effects on the Measured Nitrogen
Abundances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
v
9 Conclusions 175
9.1 ResultsofNon-LTEcalculations . . . . . . . . . . . . . . . . . . . . . . . . . 175
9.2 Gravitational DarkeningEffects . . . . . . . . . . . . . . . . . . . . . . . . . . 176
9.3 ResultsoftheAbundanceAnalysis . . . . . . . . . . . . . . . . . . . . . . . . 177
9.4 FutureDirections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Bibliography 179
A ListofConstantsandAbbreviations 187
A.1 Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
A.2 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
B multiResultsofSelectedNiilines 188
C MonteCarloResults 218
D HαFittingFigures 234
E NiiNormalizedSpectra 254
CurriculumVitae 276
vi
List of Figures
2.1 Theevolution oftherotational profileofa9M star . . . . . . . . . . . . . . . 15
⊙
2.2 Theevolution oftheH,He,C,N,andOsurfaceabundancesofa9M star . . . 16
⊙
2.3 Theevolution ofarotating9M staronthemain-sequence . . . . . . . . . . . 17
⊙
2.4 Theevolutionarytrackwithandwithoutrotationforstarswithmassesbetween
9M and120M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
⊙ ⊙
2.5 Evolutionary tracksoftheatmosphericnitrogenabundanceinmassivestars . . 19
2.6 Evolutionary tracks of the ratio of the carbon abundance to the nitrogen abun-
danceinmassivestars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7 Ioschronesforrotating andnonrotating models . . . . . . . . . . . . . . . . . 21
2.8 Thechangeoftheratiooftheangularrotational velocitytothecriticalvalue . . 22
2.9 Theincreaseofnitrogenabundancewithstellarage . . . . . . . . . . . . . . . 24
2.10 The nitrogen abundances for a sample of MagellC B and Be stars (Dunstall et
al.,2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.11 The change of the atmospheric nitrogen abundances with the change of the
rotationalvelocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1 ThedependenceoftheobservedlineprofilesofBestarsonthestellarinclination 32
3.2 colour-colour diagramforanumberofBestars . . . . . . . . . . . . . . . . . 35
5.1 NiiGrotrian diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 Quadratic stark width ratios of N ii lines versus the effective quantum number
oftheupperlevel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.3 Thefractionofsinglyionizednitrogenasafunctionoftheopticaldepth . . . . 57
5.4 RadiationtemperatureoftheionizingmeanintensityforthefirsttenlevelsofNii 58
5.5 Non-LTE departures coefficients for the first sixteen energy levels of Nii plus
thegroundlevelofNiii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.6 The predicted LTE (dashed lines) and non-LTE equivalent (solid lines) widths
ofNiiλ3995Å andλ6482Å . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.7 ThelinesourcefunctionofN iiλ3995Å λ6482Å . . . . . . . . . . . . . . . 65
5.8 HydrogenopacityeffectsonthecomputedequivalentwidthsofNiiλ6482Å and
λ3995Å . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.9 CurvesofgrowthforNiiλ6482Å andλ3995Å . . . . . . . . . . . . . . . . 67
5.10 ThesourcefunctionoftheN iiλ3995Å&λ6482Åfordifferentnitrogenabun-
dances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.11 The line source function of N ii λ 3995Å line from the results of the multi-
multianalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
vii
5.12 The line source function of N ii λ 6482Å line from the results of the multi-
multianalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.13 The distribution of the equivalent widths results of the Monte-multi analysis
forλ6482Å andλ3995Å . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.14 The uncertainties of the estimated nitrogen abundances due to inaccuracies in
theatomicdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.15 Thechangeofthecomputedequivalentwidthsofλ3995Å andλ6482Å with
thechangeofthesizeofthenitrogen atom . . . . . . . . . . . . . . . . . . . . 85
6.1 HeiGrotrian diagramshowingthesingletandtriplet spinsystems. . . . . . . . 92
6.2 ThestarkwidthratiosofHe ilinesversustheeffectivequantumnumberofthe
upperLSstate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.3 Theionization BalancesofHeiandHeii . . . . . . . . . . . . . . . . . . . . . 98
6.4 Theradiationtemperatureofthephotoionizingradiationatthethresholdwave-
lengthforthelowest10LSstatesoftheHei . . . . . . . . . . . . . . . . . . . 99
6.5 Thenon-LTEdeparturecoefficientsofthepopulationnumbersofthelowest15
LSstatesofHeiplusthegroundlevelofHeii . . . . . . . . . . . . . . . . . . 100
6.6 ThecomputedequivalentwidthsofanumberofHei(I) . . . . . . . . . . . . . 102
6.7 ThecomputedequivalentwidthsofanumberofHeilines(II) . . . . . . . . . . 103
6.8 ThecomputedequivalentwidthsofanumberofHeiλ10830Å line. . . . . . . 104
7.1 TheDistribution oftheeffectivetemperatureoverthesurfaceofarotating star . 113
7.2 The gravitational darkening effects on the predicted equivalent widths of the
N ii3995Å and6482Å lines. . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.3 Gravitationally darkening effects on the predicted equivalent widths of λ 3995
andλ6482Å Niilinesforv =0.85 . . . . . . . . . . . . . . . . . . . . . . 116
frac
7.4 Thegravitational darkeningeffectsontheequivalentwidthoftheHe iλ6678Å 117
7.5 The gravitational darkening effects on the predicted equivalent widths of the
Mg iiλ4481Å . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.6 The gravitational darkening effects on the estimated v sini using measured
equivalentwidthsoftheHeiλ6678Å andtheMg iiλ4481Å. . . . . . . . . . 120
8.1 Normalization processoftheHαlineprofileoftheBestarHD143275 . . . . . 126
8.2 NormalizedHαoftheBestarHD143275 . . . . . . . . . . . . . . . . . . . . 127
8.3 Normalization processoftheNiiλ3995.0Å lineoftheBestarHD143275 . . 128
8.4 Normalization processoftheNiiλ4447.0Å lineoftheBestarHD143275 . . 129
8.5 Normalization processoftheNiiλ5679.0Å lineoftheBestarHD143275 . . 130
8.6 NormalizedNiilinesoftheBestarHD143275 . . . . . . . . . . . . . . . . . 131
8.7 NormalizedNiilinesoftheBestarHD11415 . . . . . . . . . . . . . . . . . . 132
8.8 NormalizedNiilinesoftheBestarHD143275 . . . . . . . . . . . . . . . . . 133
8.9 Comparison of the T estimates of Levenhagen & Leister (2006) for 22 Be
eff
starsinthesamplewiththecorrespondingvaluesofFre´matetal.(2005) . . . . 137
8.10 Comparison of the T estimates of Catanzaro (2013) for seven Be stars in the
eff
samplewiththecorresponding valuesofFre´matetal.(2005) . . . . . . . . . . 138
8.11 vsinidistribution fortheBestarssample . . . . . . . . . . . . . . . . . . . . . 141
viii
8.12 FittingoftheobservedHeiλ4471Å,Mgiiλ4481Å andHeiλ6678Å lines
withsyntheticnon-LTElineprofilesoftheBestarHD11415. . . . . . . . . . . 143
8.13 FittingoftheobservedHeiandMgiilineswithsyntheticnon-LTElineprofiles
oftheBestarHD174237 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.14 FittingoftheobservedHeiandMgiilineswithsyntheticnon-LTElineprofiles
oftheBestarHD65875 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.15 FittingoftheobservedHeiandMgiilineswithsyntheticnon-LTElineprofiles
oftheBestarHD45725 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.16 FittingoftheobservedHeiandMgiilineswithsyntheticnon-LTElineprofiles
oftheBestarHD203467 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.17 Comparisonofthecurrentestimatesofloggwiththeavailablevaluesinliterature145
8.18 MeasuringequivalentwidthsofobservedNiilinesinthespectraoftheBestar
HD11415. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8.19 Measured equivalent widths of observed Nii lines in the spectra of the Be star
HD67698 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
8.20 Measured equivalent widths of observed Nii lines in the spectra of the Be star
HD58343 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.21 NormalizedHαoftheBestarHD49567 . . . . . . . . . . . . . . . . . . . . . 152
8.22 HαlinefittingoftheBestarHD189687 . . . . . . . . . . . . . . . . . . . . . 154
8.23 HαlinefittingoftheBestarHD143275 . . . . . . . . . . . . . . . . . . . . . 154
8.24 HαlinefittingoftheBestarHD45725 . . . . . . . . . . . . . . . . . . . . . . 155
8.25 ComparisonofcurrentinclinationestimationswiththoseofFre´matetal.(2005)
forthecommonobjects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.26 ResultsofKStestresultforcurrentinclinationestimationsandthoseofFre´mat
etal.(2005) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8.27 ResultsofKStestresultfortheentiresampleofFre´matetal.(2005) . . . . . . 159
8.28 TheestimationofthenitrogenabundanceoftheBestarHD56139basedonthe
measuredequivalentwidth oftheNii3995Åline. . . . . . . . . . . . . . . . . 161
8.29 NitrogenabundanceestimationsofthesampleofBestarsversustheireffective
temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
8.30 ResultsofKStestresultfortheestimatednitrogenabundancesofthesample. . 163
8.31 Comparisonoftheestimatednitrogenabundancesfromλ3995Å Niilinewith
theresultsoftheabundanceanalysisincludingallobservedNiilines . . . . . . 165
8.32 RelationbetweentheestimatednitrogenabundancesoftheBestarssampleand
theirgravities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8.33 Figure shows relation between the estimated nitrogen abundances of the Be
starssampleandtheirequatorialrotational velocities . . . . . . . . . . . . . . 167
8.34 FigureshowsthediskcontaminationasfunctionofthewavelengthforB3-type
Bestar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.35 FigureshowsthediskcontaminationasfunctionofthewavelengthforB4-type
Bestar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.36 Correctionsofthemeasurednitrogenabundancesfordiskcontamination effect 172
8.37 HistogramsofmeasuredBandBestarnitrogenabundancesfromseveralsources173
D.1 HαlinefittingoftheBestarHD33328 . . . . . . . . . . . . . . . . . . . . . . 234
ix