Determining the orbital element and absolute magnitude distribution of main belt asteroids PDF
Preview Determining the orbital element and absolute magnitude distribution of main belt asteroids
DETERMININGTHEORBITALELEMENTANDABSOLUTE MAGNITUDEDISTRIBUTIONOFMAINBELTASTEROIDS By TIMOTHYBRUCESPAHR ADISSERTATION PRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 1998 Dedicatedtomyparents. ACKNOWLEDGEMENTS Therearetoomanypeoplethathavebeenessentialtothisworktoacknowl- edgethemall,butIwilltrytoincludethemostinstrumental. BrianMarsdenhasbeen continuallysupportive. GarethWilliamswasalwaysreadytoprovideephemeridesfor newBSSobjects,anditseemedhewasalwaysconnectedtoacomputersomewhere. CarolynandGeneShoemakerwerealwayshelpful,evenaftertheGreatCometCrash hadthemcirclingtheglobetoattendmeetings. WithoutSteveLarson’shelp,assis- tance,andsupport,therewouldhavebeennoBSS.MyfriendsDave,Jo,Tony,Kirk andNicolekeptmesanebyforcingmetoplaycardsatleastonceaweek. Ithankmy goodfriendandcolleague,CarlHergenrother,forputtingupwithmeduringlong, tediousobservingrunswiththeSchmidt. FinallyIthankJoannaforhersupport, herenthusiasm,andherheart. m TABLEOFCONTENTS ACKNOWLEDGEMENTS iii ABSTRACT vi CHAPTERS 1 INTRODUCTION 1 1.1 Reasons 1 1.2 HistoryandPastSurveys 3 1.3 OrbitalElements 5 1.4 StructureoftheAsteroidBelt 7 1.5 Contents 11 2 MDS,PLSANDSPACEWATCH 20 2.1 StartingPoint: TheMcDonaldAsteroidSurvey 20 2.2 ThePalomar-LeidenAsteroidSurvey 21 2.3 InclinationLimitationofthePLS 22 222...456 TTIshhmee0SPpraaoUcbselewefamutlcwhiQtuShaunFrtoviretcyyedatEcalcle?ntricity 222334 2.7 PLS,Spacewatch,andtheCatalogedAsteroidPopulation .... 25 3 THEBIGELOWSKYSURVEY 35 3.1 WhatistheBSS?WhoWeretheMainPlayers? 35 3.2 BackgroundandMotivation 36 3.3 GeneralInformation 37 3.4 GeneralDiscussion 40 4 DEBIASINGTHEPLS 47 4.1 HowDoesDebiasingWork? 47 4.2 HowtoCalculateP? 48 4.3 TheTBSMonte-CarloMethodforDetectionProbabilities .... 49 4.4 HowDoesPVaryforaStandardField? 51 4.5 ApplicationtothePLS 52 4.6 DeterminationofthePLSVMagnitudeEfficiency 52 4i.n7EaWchhyHthBeinPLSWillUnderestimatetheTrueNumbersofAsteroids 53 4.8 TheTrendwithLongitudeofPerihelion 54 IV 4.9 Results 54 4.10 Additional 56 5 DEBIASINGTHEBSS 74 5.1 Introduction 74 5.2 GeneratedObjectsandDetectionEfficiency 75 5.3 Results 77 5.4 GeneralTrendsintheRegiona=2.6-3.3AU 77 5.5 NewFamilies 78 6 WHEREISTHEBESTPLACETOLOOKFORCERTAINTYPESOF ASTEROIDS? 86 6.1 TheGeneralConcept 86 6.2 QuantitativeStudy: EosandMariaFamilyAsteroids 86 7 SUMMARY 90 7.1 Conclusions 90 7.2 FutureWork 92 REFERENCES 95 BIOGRAPHICALSKETCH 97 v AbstractofDissertation PresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy DETERMININGTHEORBITALELEMENTANDABSOLUTE MAGNITUDEDISTRIBUTIONOFMAINBELTASTEROIDS By TimothyBruceSpahr May 1998 Chairman: Dr. StanleyDermott MajorDepartment: Astronomy Wepresentheretwogeneraltechniquestoremoveobservationalselectionef- fects fromasteroidsurveys. When appliedtotwospecific asteroidsurveys, these methodshave allowed thefirst computationofthe debiaseddistributionofaster- oidalorbitalelementsandsizesforthefirsttime. Thefirstsurveywasconducted in 1960. Advancesincomputinghaveallowedthedatatobere-analyzedusingan existingcomputerprogramandgivenamuchmorerigorousstatisticaltreatment. Thesurveywasconfinedtothenear-eclipticatopposition,thereforeitsusefulness islimitedwithregardtohighlyinclinedorbits. Tocompensateforthislimitation, weconductedourownsurveyaimedspecificallyathigh-inclinationobjects. Since theseorbitsare,ingeneral,distributeddifferentlythanlower-inclinationorbits,re- movingobservationalselectioneffectsrequiredcreatingastatisticaltechniqueusing Monte-Carlotypesimulations. vi The results ofthis work show no evidence for differingslopes ofthe size- frequencydistributionthroughouttheasteroidbelt,fromthehighlyinclinedHungaria- typeasteroidsintheinneredgeofthebelt(1.8-2.0AU),totheouterbelt3-3.5AU). Theslopesoftheabsolute-magnitudefrequencydistributions, beinglessthan0.5, showthattheasteroidalsizedistributionissomewhatshallowerthanwhatwouldbe predictedassumingtheasteroidstobeacollisionallyevolvedpopulationofbodies withsize-independentimpactstrengths. Alsodeterminedareroughnumbersofas- teroidsinthemaindynamicalfamiliesofEos, Maria,Themis, andKoronis,which compriseasignificantfractionofthetotalnumberofobjectsinthemainbelt. This workhasalsoresultedinthediscoveryofanewasteroiddynamicalfamily,andpos- siblytwonewasteroidgroups. Vll H CHAPTER1 INTRODUCTION Scientistswhowishtoobtainusefulstatisticalinformationonalargepopula- tionofobjectsarefacedwithtwochoices: observeandcatalogtheentirepopulation orobservesomesmallersampleofthewholeandscalethesedatainsomemeaningful andappropriatefashioninordertoobtaininformationaboutthewhole. Toextend theresultsofasmall-scalesurveytothewholepopulationrequiressome debiasing techniquetoremovetheobservationalselectioneffects. Thisispreciselytheprob- lemfacingastronomersstudyingasteroids. Itisestimatedthatthereareatleast 1,000,000asteroidswithdiametersgreaterthanabout1km,yetthepresentdetected populationcontainsonlyabout 50,000members. There have been manysurveys aimedspecificallyatdiscoveringandcatalogingasteroidsoverthepast50years,but veryfewhave attemptedtoremoveobservationalselectioneffectsandpredictthe totalpopulationofasteroidsdowntoagivensize. Asaresult,wehaveobservational completenessonobjectsdowntoonlyabout25km,orthoseobjectswithabsolute magnitudes,H,lessthanabout11.0. ( istheVmagnitudeoftheasteroidatthe mythicallocationof1AUfromboththeSunandtheEarthatzerophaseangle.) Theaimofthisworkistointroducetwodebiasingmethodsandapplythemtotwo differentasteroidsurveysinordertoobtainthebestestimateforthedistributionof mainbeltasteroidorbitsandsizesforthefirsttime. 1.1 Reasons Firstandforemost, thisThesisisan attempttogainabetterunderstand- ingofthenumerousobservationalselectioneffectsthatinfluence asteroidsurveys. 1 2 Whilesomegeneraltrendsarealreadyknown,thissubjectislargelyunexplored. By theconclusionofthisresearch, weshouldhaveasolidunderstandingofthemost importantselectioneffectspresentinasteroidsurveys. Perhapsthemostimportantreasonforthisworkistodeterminethemass- frequencydistributionoftheasteroids.Themassdistributionisnotobtaineddirectly, but indirectlyfrom the size distribution, or the absolute magnitude distribution. Dohnanyi (1969) found that the mass distribution ofa set ofmutually colliding bodies,allwithsize-independentimpactstrengths,couldbedescribedby: f(m)dmocm~qdm (1.1) with f(m) beingthe numberofobjectsin themassrangemtom -b dm and q, theslopeindex, = 11/6forcollisionalequilibrium. Tocomparewiththeabsolute magnitudedistribution,i.e.,aplotoflog(n)versusH,withnbeingtheincremental (andnotthecumulative)numberinabinofH,theslopesarerelatedbythefollowing equation: q=\a+l C1-2) whereaistheslopeoftheabsolutemagnitude-frequencydistribution. Inthecaseof collisionalequilibrium,a=0.5forobjectswithsizeindependentimpactstrengths. Anavaluesignificantlydifferentthan0.5,confirmingtheresultsofDurdaandDer- mott (1997),wouldplaceconstraintsonthestrength-scalinglawforasteroidsand perhapsprovideuswithcluestoasteroidalcompositionandstructure. Unfortunately, ourobservationallycompleteset(thesetofasteroidsdowntoacertainsizethatwe havediscoveredverynearlyeveryexistingmember)onlycontains2644membersand extendsonlytoH=12.5intheinnerbelt,andH=11intheouterbelt. Without debiasingtheasteroidbelttoH>13,ourobservationallycompletesetwillprovide noinformationona(andhenceq)sincethetransitiontothecollisionallyevolved 3 portionoftheasteroidbeltoccursatH~ 13(seealsoDurdaandDermott1997). Witha,orqinhand,wewillbeabletopredicttheamountofdustintheZodiacal Cloudfromasteroidsalone. Another important result to beobtained from this work will be the total numberofasteroidsinthemainfamilies. Thiscaninturnbeused,alongwithq,to predicttheamountofdustinjectedintotheZodiacalCloudfromthesemainfamilies. Theorbitalelementdistributionandnumberdensity, particularlyforthose objects near resonances, will allow us to get a direct estimate ofthe number of objectsonunstableorbits,andthusanestimateofthenumberofobjectsrequiredto replenishtheseareas. IftheexpectednumberofNear-EarthObjects (NEOs) from this type ofanalysisis toosmall, it willindicate asignificant numberofextinct cometsexistintheNEOpopulation. High-inclinationasteroidsarealwaysundersampledbyeclipticsurveys. The absolutemagnitudedistributionoftheseobjectswillbeofimportancetodetermine whether ornot thesize distributionisdifferentthan that ofotherregions ofthe asteroidbelt,asthesehigh-inclinationobjectscollidelessfrequentlythanotherob- jects,butdosowithmuchhighermeanimpactvelocities. Becausetherearesofew highinclinationobjectsintheobservationallycompleteset, asurveythatpresents thedebiasedorbitalelementdistributionofthesehigh-inclinationobjectswllbeof usesimplysothatwecan,forthefirsttime,viewtheorbitalelementdistributionof theseobjects. 1.2 HistoryandPastSurveys Surveyingforasteroidshastakenplaceonandofffornearly200years. In September 1800 the infamous “Celestial Police” met to discuss searching for the mythicalmissingplanetbetweenMarsandJupiter. These24astronomerschoseto dividetheeclipticin15degreeswathes,andsearchedforthemissingplanetvisually.
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