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The Primordial Binary Population in the Association Sco OB2

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The Primordial Binary Population in the Association Sco OB2 The primordial binary population in the association Sco OB2 arXiv:astro-ph/0610792v1 26 Oct 2006 Cover illustration: a large fraction of the stars is known to be in binary or multiple systems. It is therefore likely that many exoplanets have more than one Sun in the sky. The cover illustration represents an imaginary landscape on a planet in such a system. The original photograph shows the surface of the planet Mars, obtained with the exploration rover Spirit; courtesy of NASA/JPL/Cornell. The primordial binary population in the association Sco OB2 De oorspronkelijke dubbelsterpopulatie in de associatie Sco OB2 Academisch Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam, op gezag van de Rector Magnificus prof. mr. P. F. van der Heijden, ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Aula der Universiteit op donderdag 28 september 2006, te 12:00 uur door Mattheus Bartholomeus Nicolaas Kouwenhoven geboren te Kwintsheul P P prof. dr. L. Kaper prof. dr. E.P.J. van den Heuvel C- dr. A.G.A. Brown dr. S.F. Portegies Zwart O prof. dr. H.F. Henrichs dr. A. de Koter prof. dr. L.B.F.M. Waters prof. dr. R.A.M.J. Wijers prof. dr. P.T. de Zeeuw dr. H. Zinnecker Faculteit der Natuurwetenschappen, Wiskunde en Informatica Het hier beschreven onderzoek werd mede mogelijk gemaakt door steun van NWO. ISBN–10: 90–6464–033–5 ISBN–13: 978–90–6464–033–9 Printed by Ponsen & Looijen, Wageningen. Copyright 2006 c Thijs Kouwenhoven. Contents 1 Introduction 1 1.1 Observationalchallenges . ... 3 1.2 RecoveringthetruebinarypopulationinScoOB2 . ........ 6 1.2.1 Outlineofthisthesis .......................... 8 1.2.2 Futurework............................... 10 2 Close visual companions to A star members of Scorpius OB2 13 2.1 Introduction................................... 14 2.2 Observationsanddatareduction . .... 16 2.2.1 Definitionofthesample . 16 2.2.2 Observations .............................. 16 2.2.3 Datareductionprocedures . 18 2.2.4 Componentdetection. 19 2.2.5 Photometry............................... 20 2.3 Backgroundstars ................................ 21 2.4 Propertiesofthecompanionstars. ..... 27 2.4.1 Generalproperties .... .... .... ... .... .... .... 27 2.4.2 Color-magnitudediagramandisochrones . .... 28 2.4.3 Massesandmassratios. 31 2.5 Comparisonwithliteraturedata. ..... 35 2.5.1 Newcompanions............................ 35 2.5.2 Binarystatistics............................. 38 2.6 Conclusionsanddiscussion. ... 39 AppendixA:ResultsoftheADONISbinaritysurvey . ....... 41 3 A brown dwarf desert for intermediate mass stars in Sco OB2? 51 3.1 Introduction................................... 52 3.2 Observationsanddatareduction . .... 54 3.2.1 DefinitionoftheNACOsample . 54 3.2.2 NACOobservations ... .... .... ... .... .... .... 54 3.2.3 Datareductionprocedures . 56 3.2.4 Componentdetection. 57 3.2.5 Photometry............................... 58 3.2.6 Photometric precision and accuracy of the NACO observations. 58 3.2.6.1 Algorithmprecision . 58 3.2.6.2 Comparisonwith2MASS . 59 i ii CONTENTS 3.2.6.3 Comparison with the ADONIS survey of Kouwenhoven etal.(2005a)......................... 59 3.2.6.4 ComparisonwithShatsky&Tokovinin(2002) . 60 3.2.7 GeneralpropertiesoftheNACOobservations . ..... 60 3.3 The completeness and detection limit of the ADONIS and NACOsurveys . 61 3.4 Statusofthestellarcomponents . .... 63 3.4.1 Color-magnitudediagramandisochrones . .... 63 3.4.2 Distinction between companions and background stars ........ 64 3.4.3 Thebackgroundstarpopulation . 67 3.4.4 Notesonsomeindividualsecondaries . ... 71 3.4.5 Accuracyof the KS = 12separationcriterion . 73 3.5 Massesandmassratios ... ... .... .... .... ... .... .... 74 3.6 Thelowerendofthecompanionmassdistribution . ........ 74 3.6.1 Thebrown dwarf “gap”for 1′′ ρ 4′′ ................ 74 3.6.2 Arealbrowndwarfdesert?. .≤ . .≤ . 76 3.6.3 Theoriginofthebrowndwarfdesert. .. 80 3.7 BinarityandmultiplicityinScoOB2 . ..... 83 3.8 Conclusions................................... 84 AppendixA:ResultsoftheNACObinaritysurvey. ....... 86 4 Recovering the true binary population from observations 99 4.1 Introduction...................................100 4.2 Methodandterminology . 102 4.2.1 SimulatingobservationsofanOBassociation . ......104 4.2.2 Distributionfunctions . 106 4.2.3 Statisticaltestsanderrorcalculation . .......106 4.2.3.1 Comparisonbetweentwodistributions . 107 4.2.3.2 Comparisonbetweentwobinaryfractions . 107 4.2.4 Theerroronthebinaryfraction . 107 4.3 Conversiontoobservables . 108 4.3.1 Visualbinaryobservables . 108 4.3.2 Spectroscopicbinaryobservables . 109 4.3.3 Astrometricbinaryobservables . 110 4.3.4 Photometry ...............................110 4.4 Associationandbinarypopulationproperties . .........110 4.4.1 Choiceofbinaryfraction. 111 4.4.2 Choiceofassociationdistance,size,andage . ......112 4.4.3 Choiceofmassdistribution . 113 4.4.4 Choice of pairing function and mass ratio distribution.........116 4.4.5 Thesemi-majoraxisandperioddistribution . ......117 4.4.6 Theeccentricitydistribution . 120 4.4.7 Choiceoforientationandphaseparameters . 120 4.5 Observational selection effects .........................121 4.5.1 Theobserver’schoice . 121 4.5.2 Visualbiases ..............................122 4.5.2.1 Thebrightnessconstraintfor visualbinaries . 122 4.5.2.2 Theseparationconstraintfor visualbinaries . 123 CONTENTS iii 4.5.2.3 Thecontrastconstraintforvisualbinaries. 123 4.5.2.4 Theconfusionconstraintforvisualbinaries . 124 4.5.2.5 Theerrorsonthevisualbinaryobservables . 124 4.5.3 Spectroscopicbiases . 124 4.5.3.1 The brightness constraint for spectroscopic binaries . 125 4.5.3.2 The instrument bias for spectroscopic binaries: method 1 (SB-S) ............................125 4.5.3.3 The instrument bias for spectroscopic binaries: method 2 (SB-C)............................126 4.5.3.4 The instrument bias for spectroscopic binaries: method 3 (SB-W) ...........................128 4.5.3.5 AcomparisonbetweenSB-S,SB-C,andSB-W . 129 4.5.3.6 The sampling constraint for spectroscopic binaries. ....130 4.5.3.7 The errors on the spectroscopic binary observables . 131 4.5.4 Astrometricbiases . 131 4.5.4.1 The brightness constraint for astrometric binaries .....132 4.5.4.2 Theinstrumentbiasforastrometricbinaries . 133 4.5.4.3 The errors on the astrometric binary observables . 133 4.6 Simulatedobservations . 133 4.6.1 Thedistancetotheassociation . 133 4.6.2 Thesizeoftheassociation . 137 4.6.3 Theorientationoftheorbits . 139 4.6.4 Theeccentricitydistribution . 140 4.6.5 Themassdistributionandpairingfunction . 141 4.6.6 Thesemi-majoraxisandperioddistributions . ......146 4.6.7 Thebinaryfraction . 150 4.7 The inverse problem: deriving properties from observations. 151 4.7.1 Recovering the mass distribution and pairing function ........151 4.7.1.1 The accuracy of a power-law fit to a mass ratio distribution 153 4.7.2 Recovering the semi-major axis and period distributions .......155 4.7.2.1 Discriminating between Opik’s¨ law and a log-normal pe- rioddistribution . 157 4.7.3 Recoveringtheeccentricitydistribution . .......159 4.7.4 Recoveringthebinaryfraction . 160 4.7.5 A strategy to derive the true binary population from observations . 161 4.8 An example: recovering the true binary population from simulateddata . 162 4.8.1 Simulatedobservations. 163 4.8.2 Finding the pairing function and mass ratio distribution. 163 4.8.3 Finding fa(a)..............................165 4.8.4 Finding fe(e) ..............................166 4.8.5 Findingthebinaryfraction . 166 4.8.6 Therecoveredbinarypopulation . 168 4.9 Summaryandoutlook..............................168 AppendixA:Theprojectionofabinaryorbit . ......170 4.9.1 TheEquatorialcoordinatesystem . 171 4.9.2 Theorbitorientationvectors . 172 4.9.3 Theradialvelocitycurve . 174 iv CONTENTS 4.9.4 Thefullprojectiononthesky . 175 4.9.5 Radialvelocitystatistics . 175 AppendixB:Thepairingfunction . 177 4.9.6 PairingfunctionRP. 177 4.9.7 PairingfunctionPCRP . 180 4.9.8 PairingfunctionPCP-I . 181 4.9.9 PairingfunctionPCP-II. 181 4.9.10 PairingfunctionPCP-III . 183 AppendixC:Thetotalmassofastellargrouping . .......183 AppendixD:Orbitalsizeandshapedistributions . .........185 5 Recovering the binary population in Sco OB2 189 5.1 Introduction...................................189 5.2 Methodandterminology . 191 5.3 TheScoOB2association . 191 5.3.1 ThemodelforScoOB2 . 192 5.3.2 Photometry ...............................193 5.3.3 ScoOB2membership . 193 5.4 ObservationsofbinarysystemsinScoOB2 . 195 5.4.1 KO5—Kouwenhovenetal.(2005a)observations . 197 5.4.1.1 TreatmentoftheKO5dataset . 200 5.4.1.2 ModelingtheobservationalbiasofKO5 . 201 5.4.2 KO6—Kouwenhovenetal.(2006a)observations . 202 5.4.2.1 TreatmentoftheKO6dataset . 202 5.4.2.2 ModelingtheobservationalbiasofKO6 . 203 5.4.3 SHT—Shatsky&Tokovinin(2002)observations . 204 5.4.3.1 TreatmentoftheSHTdataset . 204 5.4.3.2 ModelingtheobservationalbiasofSHT . 205 5.4.4 LEV—Levatoetal.(1987)observations . 206 5.4.4.1 TreatmentoftheLEVdataset . 206 5.4.4.2 ModelingtheobservationalbiasofLEV . 207 5.4.5 BRV—Brown&Verschueren(1997)observations . 207 5.4.5.1 TreatmentoftheBRVdataset . 207 5.4.5.2 ModelingtheobservationalbiasofBRV . 208 5.4.6 HIP— Hipparcos observations . 208 5.4.6.1 Treatmentof the Hipparcos dataset . 209 5.4.6.2 Modeling the observational bias of Hipparcos .......209 5.5 Recoveringthetruebinarypopulation . ......210 5.5.1 Recovering the pairing function and mass ratio distribution . 210 5.5.2 Recovering the semi-major axis
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