RESEARCH CAPABILITIES OF BYU‐IDAHO TELESCOPE AND …those whose apparent brightness changes with...
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RESEARCH CAPABILITIES OF BYU‐IDAHO TELESCOPE AND VARIABLE STAR STUDY OF RV URSA MAJOR by Scott Fuller Submitted to the Department of Physics in partial fulfillment of graduation requirements for the degree of Bachelor of Science Brigham Young University – Idaho December 2010 Advisor: Stephen McNeil Signature: ________________________ Committee Member: Brian Tonks Signature: ________________________ Thesis Coordinator: David Oliphant Signature: ________________________
Transcript of RESEARCH CAPABILITIES OF BYU‐IDAHO TELESCOPE AND …those whose apparent brightness changes with...
RESEARCHCAPABILITIESOFBYU‐IDAHOTELESCOPEAND
VARIABLESTARSTUDYOFRVURSAMAJOR
by
ScottFuller
SubmittedtotheDepartmentofPhysicsinpartialfulfillmentofgraduation
requirementsforthedegreeofBachelorofScience
BrighamYoungUniversity–Idaho
December2010
Advisor:StephenMcNeil
Signature:________________________
CommitteeMember:BrianTonks
Signature:________________________
ThesisCoordinator:DavidOliphant
Signature:________________________
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Abstract TheBYU‐IdahoPhysicsDepartmentrecentlyacquireda250mmf/4Maksutov
Newtoniantelescopeforusebyundergraduatesandfaculty.Inorderforstudentsto
obtainqualityimagesthatcanbeusedforresearch,theymustunderstandseveral
techniques.Thesetechniquesincludefocusing,autoguiding,andimagereduction.
ImagesaretakenwithaSBIGST‐7XMEcharge‐coupleddevice(CCD).CCDsare
employedinmanymodernastronomicalresearchprojects.TheCCDsolid‐statedesign
allowsfordetailedphotometricstudiessuchasvariablestarstudies.Variablestarsare
thosewhoseapparentbrightnesschangeswithrespecttotheobserver.RVUrsaMajor
isonesuchstar.FollowingdetailedresearchofRVUrsaMajor,itsperiodwasfoundto
be0.46746±0.00395days.Thephasecurveofthestarwasalsocreatedbasedonthe
resultsofimagestakenoveran11‐dayperiodinAugust2010.Thisresearchisdesigned
toguidefutureprojectsbyBYU‐Idahoundergraduatesandfacultymembers.
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Acknowledgments
IwouldliketoacknowledgeDr.StephenMcNeilformentoringmeandproviding
theinformationandequipmentneededtoproceedwiththisproject.Iwouldalsoliketo
thankDr.TomDavisforhisassistanceinsettingupthetelescopeandsharinghis
knowledgewithusthroughouttheproject.TheentireBYU‐IdahoPhysicsDepartment
shouldbethankedfortheircontinuedpatienceinteachingandeducatingmyselfand
otherundergraduatephysicsstudents.MostimportantlyIwouldliketothankmywife,
Traci,forbeingsupportiveofthisproject,whichrequiredmanylongnightstobespent
awayfromhomewhileshetookcareofourson,whichisneveraneasytask.
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TableofContents
ChapterI.Introduction ................................................................................................................ 11.1CCDTechnology.....................................................................................................................................11.2CCDResearchCapabilities ................................................................................................................3
ChapterII.PreparingTelescopeforOperation ................................................................... 42.1PreviousWork........................................................................................................................................42.2DailySet‐UpProcedures ....................................................................................................................42.2.1ConnectingtheST‐7XECCDCamera....................................................................................42.2.2ConnectingCameratoCCDSoftware...................................................................................62.2.3UsingTheSkySoftware ..............................................................................................................8
ChapterIII.CCDImagingTechniques....................................................................................113.1Focusing .................................................................................................................................................113.2Auto‐Guiding ........................................................................................................................................133.3ImageCalibration...............................................................................................................................153.3.1BiasImages...................................................................................................................................153.3.2DarkFrames ................................................................................................................................163.3.3Flat‐Fields .....................................................................................................................................163.3.4MasterCalibrationImage.......................................................................................................17
ChapterIV.Photometry .............................................................................................................204.1VariableStars.......................................................................................................................................204.2ObservingVariableStars ................................................................................................................224.3AperturePhotometryMeasurements .......................................................................................23
ChapterV.RVUrsaMajorVariableStarStudy ...................................................................285.1Results.....................................................................................................................................................295.2AnalysisofResults.............................................................................................................................31
ChapterVI.ConclusionandFutureResearch .....................................................................336.1Findings..................................................................................................................................................336.2FutureResearch..................................................................................................................................33
AppendixA—RVUrsaMajorStarChart ...............................................................................36
AppendixB—Data........................................................................................................................37AppendixC—CalculatingUncertainty...................................................................................42
AppendixD—TelescopeSetupSteps ...................................................................................43
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LISTOFFIGURES
1.AnatomyofaCharged‐CoupledDevice
2.OrientationofCCDCamera
3.CCDCamerawithConnectedCables
4.CCDSoftCameraControlWindow
5.ProperlyConnectedGTDControlPanel
6.TheSky6ObjectInformationWindow
7.CCDSoftFocusToolsWindow
8.FocusingKnobs
9.CCDSoftAutoguideMenu
10.MasterBiasFrame
11.MasterFlatField
12.M‐92BeforeReduction
13.M‐92AfterReduction
14.StarFieldwithIndicatedVariable,Reference,andCheckStars
15.MaximDLPhotometryTool
16.RVUrsaMajorMagnitudesfor11DaysinAugust2010
17.RVUrsaMajorPhaseCurve
LISTOFTABLES
1.RVUrsaMajorObservedMaximaDuringObservationPeriod
2.AveragePeriodofRVUrsaMajor
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ChapterI.Introduction
Astronomyisoneofthemostancientofallofthesciences.Thestars,planets,
andothercelestialobjectsthatspantheskieshavelonginterestedmankind.
Technologicaladvancesduringthepastcenturyhaveallowedscientiststomore
accuratelystudythemakeupofstars,galaxies,andnebulae.Charge‐coupleddevices
(CCDs)areonesuchinnovation.
CCDswereoriginallydesignedtoenhancecomputermemorysystemsby
allowingthecomputertostoreanyvoltagevaluewithinthedevice’srange,rather
thanjustbinarynumbers.[1]Thechipswerelaterdiscoveredtobeanimpressive
wayofrecordingimages.Today,thetechnologybehindCCDsisimplementedinthe
majorityofastronomicalstudies.
BrighamYoungUniversity‐Idahorecentlyacquireda250mmMaksutov‐
Newtoniantelescopetoassiststudentsinperformingdetailedsurveysof
astronomicalobjects.Theimagingdevicereferencedtothroughoutthispaperisthe
SBIGST‐7XME.TheST‐7XMEcontainstwoCCDchips,oneforimagingandthe
otherforauto‐guiding.Thisequipmentwillallowfuturestudentstoperforma
varietyofastronomicalstudiesandmakesignificantandmeaningfulcontributions
tomodern‐dayscience.
1.1CCDTechnology
CCDsareintegratedcircuitsthatrelyonthesemi‐conductivepropertiesof
silicon.ScientistsatBellLaboratoriesoriginallydevelopedthetechnologyinthe
1960sasamethodofreplacingexistingcomputermemorystoragedevices.The
technologyprovedtobeunsuccessfulasamemorystoragedevice;however,itwas
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soondiscoveredtobehighlycapableofconvertinglightenergy(photons)intoan
electriccharge.
WhenenergystrikesasiliconCCDphotodiode,electronsareexcitedoutofthe
valenceshellofthesilicon.Thedepletionlayerofthesiliconstoresthisfree
electron.[2]Duringastronomicalobservations,theCCDlensremainsopenfora
periodoftimewhilealargenumberofphotonsstriketheCCDchip.Astimepasses,
moreandmorephotonsexciteelectronsalongthesiliconlattice,creatingalarger
numberofelectronsstoredwithintheindividualpotentialwells.Uponcompletion
oftheimagingprocess,thetotalchargestoredineachpotentialwellistransferred
throughCCDgatesandconvertedintoadigitalunitknownasanAnalogDigitalUnit
(ADU).
Animportanttermassociatedwiththeprocessofconvertingelectricalchargeto
anADUvalueisCCDGain.ThegainofaCCDisdefinedasthetotalnumberof
electronsinafullwelldividedbythemaximumADUvaluepossibleforeachpixel:
€
Gain =Electrons in FullWell
Maximum ADUValuePossible (1)
Forexample,theBYU‐ICCDcamerahasamaximumADUvalueof65,535perpixel.
Themaximumnumberofelectronsthatcanbeheldwithinasinglepixelisaround
90,000.Solvingtheequationforgainyieldsavalueof1.37.Thismeansthatevery
1.37electronscapturedbyasinglepixelincreasestheADUofthatpixelby1.These
numbersshowthepowerandprecisionofcharged‐coupleddevices.
AcomputerequippedwithCCDimagingsoftware,suchasCCDSoft,receivesthe
ADUvalueforeachpixelandcreatesanimagebasedonthevaryingvaluesofeach
individualpixel.
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1.2CCDResearchCapabilities
CCDimagingallowsastronomersandastrophysiciststomoreaccuratelystudy
thestarsandothercelestialobjects.Alongwithtaking“prettypictures”,CCDsare
idealforphotometryandspectroscopy.Photometryisabasicastronomicalpursuit
andisdefinedasresearch“todeterminetheamountandtemporalnatureoftheflux
emittedbyanobjectasafunctionofwavelength.”[3]Insimplerterms,photometry
isthestudyoftheamountoflightemittedfromagivencelestialobject.
Photometrywillbediscussedinmoredetailinalaterchapter.Astronomical
spectroscopyistheapplicationofspectrographictechniquestocelestialobjects.
Astrophysicistsareabletodeterminethechemicalandphysicalconstructionof
distantobjectsbasedontheiremittedspectrallines.Thetopicofspectroscopywill
notbedetailedinthispaper.*
*ThetopicofastronomicalspectroscopyisdiscussedinOpticalAstronomicalSpectroscopy(Kitchin,C.R.)foundinDavidO.McKayLibrary.
Figure1:AnatomyofaChargedCoupledDevice(CCD).Imageobtainedfromhttp://micro.magnet.fsu.edu
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ChapterII.PreparingTelescopeforOperation
2.1PreviousWork
BYU‐Idaho’stelescopewasobtainedin2008andstudentworkbeganinthe
summer,2010.CameronJones,agraduateofBYU‐Idaho,wasthefirststudentto
workwithandsetupthetelescope.Theculminationofthisprojectwasawritten
manualintendedtoassistfuturestudentsinproperlysettingup,balancing,and
aligningthetelescope.[4]ThismanualcanbeobtainedfromtheBYU‐IdahoPhysic’s
department.
2.2DailySet‐UpProcedures
Oncethetelescopeisproperlymounted,balanced,andalignedaccordingto
instructionsgiveninAstrophotographyUsingtheBrighamYoungUniversityIdaho
MakNewtTelescope,theequipmentshouldnotneedtobeadjustedunlessitis
bumpedormoved.Usersofthetelescopewillsimplyneedtofollowthe“Daily
Procedures”thatarenotedinthisdocument.
2.2.1ConnectingtheST‐7XECCDCamera
ConnectingtheCCDdevicetothecomputerandtothetelescopeproperlyis
essentialinordertotakequalityimages.Thefollowingstepsoutlinehowtoconnect
thedeviceproperly:
1.Attachthe9‐PinendoftheKeyspancabletooneoftheRS‐232serialport
connectionsoftheGTDControlpanel.
2.AttachtheUSBendoftheKeyspancabletothebottomUSBportonthelaptop
computer.
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3.Removethewhiteprotectivecoverfromthetelescope’seyepiece.Ifviewingwith
theCCDcamera,alsoremovethefirstadapterfromthetelescope’seyepiece.
4.RemovetheblackprotectivecapfromtheCCDCamera.
5.FittheCCDCameraontothetelescope’seyepiecesothatthetwobarsontheback
ofthecameraareparalleltothetelescope’sopticaltube.SeeFigure2.Securely
tightenthepinthatholdsthecamerainplace.
6.Attachcamera’spowersupplyboxtotheCCDcameraandensurethatitscordis
properlypluggedintoanelectricaloutletfromtheobservatory.
7.AttachthewhitecablethatleadsfromtheGTDControlPanel’sMotor/Autoguider
portintotheCCDCamera.
8.AttachtheblackUSBcableintotheportlabeled“USB”ontheCCDCamera.
TheotherendoftheUSBcableconnectsintotheschool’slaptoponthetopUSBport.
TheportsonthecamerashouldlooksimilartoFigure3.
Figure2:ProperorientationforCCDcameraattachedtotelescope'sopticaltube.
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2.2.2ConnectingCameratoCCDSoftware
Thereareseveralsoftwareprogramsthatcanbeusedtoautomaticallyimage
usingCCDdevices.TheschoolcurrentlyhasaccesstoCCDSoft5andMaximDL4.
Bothsoftwarepackagesareusedbyprofessionalsandonlyvaryslightly.Userscan
explorebothpackagesanddeterminewhichtheyaremorecomfortablewith.The
followinginstructionsaremeanttoassistusersinconnectingtheCCDdevicetothe
school’scurrentcomputer:[5]
1.Ontheschool’scomputeropenupeitherMaximDL4orCCDSoft(oranyother
CCDimagingsoftwareyouprefertouse).∗
2.IntheCCDSoftToolbar,clickCamera>>Setup.The“CameraControl”window
shouldopen.SeeFigure4.
∗TheseinstructionswillrefertoCCDSoftsoftware.MaximDL4issimilartoCCDSoftandthesetupcanbefollowedalmostidentically,withafewminoradjustments.
Figure3:ProperlyconnectedCCDcamerawithautoguidingcable,USBcable,andpowersupplycableallattached.
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3.Inthe“Setup”tabclickonthebuttonlabeled“Connect”.ThiswillconnecttheCCD
cameratothecomputerandallowyoutooperateitfromthecomputer.Ifanerror
messageisreceived,checktomakesurethatpowerisrunningtothecameraand
thatyoucanheartheinternalfanrunning.Thepowercanalsobeswitchedoffand
thenonagaintoresetthecamera.
4.IntheSetuptab,clickthebuttonlabeled“Temperature”.
5.EnterthedesiredtemperaturefortheCCDcamera.*
6.Connectthetelescope’spowersupplytotheportlabeled“12V”ontheGTD
ControlPanel.Ifproperlyconnected,theredLEDbulbshouldbeonjustabovethe
cables.
7.ConnecttheAstro‐PhysicshandcontrollertotheGTDControlPanel.TheGTD
ControlPanelshouldlooksimilartoFigure5.
*TheCoolerPowerwillinitiallygoto100%whileitisachievingdesiredtemperature.Oncethecameraiscooled,youshouldsetatemperaturethatonlyrequires75‐80%ofthecamera’scoolingcapacity.IftheCoolerPowerpercentageishigherthanthis,setahighercoolingtemperature.Atnight,thetemperaturewillgenerallybebetween‐5.00and‐20.00C.Everynightwillbedifferent,dependingontheambienttemperature.
Figure4:CCDSoftCameraControlwindow.
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8.OntheAstro‐Physicshandcontroller,select“Location1”andenterGOTObutton.
9.OntheAstro‐Physicshandcontroller,select“ResumeRef‐Park1”.
10.Onthedesktopoftheschool’scomputeropenup“TheSky6.”
11.InTheSky6clickTelescope>>Link>>Establish.
12.Makesurethatthecomputer’sclockissetcorrectlyandensurethatTheSkyis
usingthecomputer’sclockbyclickingonthe“UseComputer’sClock”icon.
13.Setyourviewingorientation(generallywiththezenithup)byclickingon
“Orientation”andthenselectingpreferredorientation.
2.2.3UsingTheSkySoftware
TheSky6ProfessionalEditionisanastronomyprogramdesignedto
automaticallycontrolamateurandprofessionaltelescopes.Theprogramcontains
manyfeaturesincludingaplanetariumviewthatdepictsarealisticskythatmoves
overtimeinordertosimulatethemotionofcelestialobjects.Whenusedtogether
withcertaintelescopemounts(suchastheGTOseriesmountattheBYU‐Idaho
livestockcenter),TheSkycanautomaticallypointuserstospecificobjects.[6]
Figure5:ProperlyconnectedGTDControlPanel.
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TherearemanyfeaturesinTheSkythatmaketelescopeoperationeasierand
moreeffective.Thefollowinginstructionsaredesignedtobeassistinthebasic
setupofTheSky.Usersshouldlearnhowtomoreeffectivelyusethesoftwareto
meettheirownneeds.
1.InTheSky6,selectabrightobjectwellEastofthemeridian.Theobjectshouldbe
highintheskyandfairlybright.
2.Aboxlabeled“ObjectInformation”shouldopen.Inthe“Telescope”tab(see
Figure6)clickonthe“Slew”icon.Thetelescopeshouldbegintomovesothatit
pointsattheobject.*
3.InCCDSoft,clickonthe“FocusTools”tab.MakesurethattheImagerisbeing
used,relativelyshortexposures(lessthan2seconds)areset,aBinningsettingof
1x1isselected,andaDelayofaround2‐4seconds.MakesurethattheContinuous
boxisnotchecked.
4.Click“TakeImage”.Thiswilltakeasingleimageandallowobserverstoinspect
whetherornotthedesiredobjectisinfactatthecenterofthetelescope’sfieldof
view.*Whileslewing,makesurethatnoneofthecablescatchonanything.Evenifyouaresurethateverythingissecurelyfastened,itisagoodideatostandbythetelescopeandmakesurethatthemanycablesdonotcatchandpulloutthecameraorknockoverthescope.
Figure6:TheSky6’s"ObjectInformation"window.
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5.InthetoolbarclickImage>>ShowCrossHair.Thiswillcreateasetofcrosshairs
thatwillallowtheusertomoreaccuratelydetermineiftheobjectisinfactatthe
centerofthecamera.
6.Inthe“Focus”tab,marktheboxlabeledContinuousandthenclick“StartFocus.”
Thecamerawillnowtakecontinuousimageswhiletheobjectiscentered.
7.UsingtheAstro‐Physicshandcontroller,movethetelescopeslightlysothatthe
objectatthecenterofthecrosshairs.
8.Ifyouhavehadtomovethetelescopeinordertocentertheobject,gobackto
TheSky6andclickontheobjectagain.Aboxlabeled“ObjectInformation”shouldbe
availablewithseveraltabs.Clickthe“Telescope”tabandthenclick“Sync”.Thistells
thetelescopethatitisnowaccuratelypointingatthatpositioninthesky.
9.Ifthetelescopewasmoved,itisagoodideatomovetoafainterobjectinthesky
(magnitude5or6),andrepeattheprocessofcenteringtheobjectonthecamera.
UsersshouldremembertoSyncthetelescopeagainifthetelescopewasmovedwith
thehandcontroller.Ifthetelescopeisevenslightlyoffoftheobject,itwillslowly
driftfromdesiredpositionsasitslewsacrossthesky.
Observersshouldnowbeabletoclickonanyobjectintheskyandclickthe
“Slew”button.Ifthetelescopehasbeenproperlysyncedthetelescopetothe
computer,theobjectshouldbeverynearthecenterofthecamera’sfieldofview.
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ChapterIII.CCDImagingTechniques
3.1Focusing
FocusingtheCCDdeviceisanessentialprocedureinordertoobtainquality
images.Thefollowingguidelinesaredesignedtoinstructuserswhowillmanually
focusthetelescopeusingCCDSoft5orMaximDL4.Userswhohaveaccesstoan
automaticfocuserwillrequiretheaidoftheuser’sguidethataccompaniesthe
focuser.
Oncethetelescopeispointedatthedesiredobject,userswillproperlyfocusthe
telescope.Withoutproperfocusing,objectsmayappearblurryandnotassharp.The
followinginstructionsaredesignedtoassistusersinachievingqualityfocus:
1.PointthetelescopetoadesiredregionintheskyusingTheSky6.
2.InCCDSoft,openupthe“FocusTools”tabandmakesurethefollowingsettings
areachieved(seeFigure7):
A.TheImagerismarked.
B.Settheexposuretimebetween0and5seconds.Dependingonthe
brightnessofyourobject,youwillhavevaryingexposuretimes.
C.Setbinningto1x1.
D.SettheDelaybetween3and5seconds.
E.TheContinuousboxshouldbemarked.
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3.Nowclickonthe“ClearGraph”button.
4.SettheGraphto“Sharpness”.
5.Select“TakeImage”.Thecamerawillbegintotakeaseriesofimages.
6.Manuallyadjustthefocusduringdelayperiodsinordertoachievethehighest
possiblesharpnessvalue.Beginwiththelargefocusknobuntilthestarslooklike
roundballs,andthenusethefinefocustoachievethehighestsharpnessvalue.As
thesharpnessincreasesagreaterfocusisachieved.Thestarsshouldlooklikesmall
roundballs.
Figure7:ScreenshotofCCDSoft's"FocusTools"window.
Figure8:BYUITelescope'sfocusingknobs.Thetwoblackknobsonthesidearetheroughfocuserswhilethegoldknobisthefinefocuser.
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7.Asubframecanalsobecreatedtoviewsmallerstarsbyclickingonaprevious
imageandcreatingabox.Thiswillallowtheusertofocusinonaspecificstarrather
thananentirefieldofview.
8.Whenfinished,click“Abort”.
Onceadequatefocusisachievedtheobservercanproceedtoimaging.
3.2Auto‐Guiding
TheBYU‐IdahoCCDcontainstwodifferentcameras.Oneofthecameras
performsimagingwhiletheotherautoguides.Eventhemostaccuratelyaligned
telescopewilleventuallyencounterpointinganddriftingerrors.Auto‐guidingis
straightforwardandprovidesextremelyhighbenefits.CCDSoft’sauto‐guiding
featureassistsinmeasuringthepositionofastaronthetrackingCCDeveryfew
seconds.Ifthestarmovesonthechipbetweenexposures,CCDSoftsendsasignalto
themounttomoveagivendirection,correctingthepointingerror.
Therearetwostepsinvolvedincorrectlyauto‐guidingduringimaging.Thefirst
stepistocalibratethemountandthesecondistoselectaguidestarandbeginauto‐
guiding.Thefollowingstepswillassistusersinemployingtheauto‐guidingfeatures
oftheBYU‐Idahotelescope:
1.OpentheCameraControlPanelandopentheAutoguidetab.
2.Positionabrightstarontheguidedetector.Ideallytherewillnotbeanotherstar
withsimilarbrightnessonthedetector.
3.ClickTakeImageandthenclickontheguidestar.
4.ClickCalibrate.Theprogramrunsforafewminutesandwillinformtheuserif
calibrationwassuccessfulornot.Ifusersreceiveanerrormessage,theXandY
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calibrationtimescanbeadjusted.Diagnosisofmosterrorscanbefoundinthe
CCDSoftUser’sManual.*
5.ClickTakeImagetoconfirmthepositionoftheguidestar.Then,clickontheguide
star.
6.Setanexposuretime.Typicallythisvaluewillbebetween3‐5seconds,butcanbe
longeriftheguidestarisnotbrightenough.
7.ClickAutoguidetostarttheautoguidingprocess.[5]
Auto‐guidingisnotnecessaryforallimages.Mostlongimagingsessionswill
provetobemoreusefuliftheauto‐guidingfeatureisemployed,sincestarswill
remaininthesamespotontheCCDchip.Additionalinformationcanbefoundinthe
CCDSoftUser’sManual.
*UsersshouldbeawarethattheAutoguidingfeatureisnotsuccessfulwhileusingtheLuminanceFilterontheschool’sfilterwheel.Thefilterdoesnotallowenoughlighttoenterthetrackingchipinsidethecamera.
Figure9:TheCCDSoftAutoguidemenu.
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3.3ImageCalibration
DuetothehighsensitivityofCCDdevices,theyaresubjecttovarioustypesof
errorsduringimaginganddataprocessing.Theseerrorstypicallyresultin
additionalelectronsbeingstoredinseveralofthepotentialwells.Theseelectrons
maybetheresultofthermalheatacquiredasthedataprocessingtakesplaceor
fromotherinternalsources.Whiletheseelectronsdonotoriginatefromstarlight,
differentiatingthemfromphotoelectronsprovesimpossible.Imagecalibration
assistsastronomersinreducingtheseerrors.Therearethreespecifictypesof
calibrationimages:biasimages,darkframes,andflatfields.
3.3.1BiasImages
Abiasframeisanimagetakenwithazero‐secondexposuretime.TheCCD
shutterremainsclosedwhiletakingabiasimage.Theresultisanimagethat
containsanunderlyingnoiselevelthatisaccompaniedbyeachrawimage.This
noiseistheresultofreadingoutdatafromthecameratothecomputerthatincludes
convertingthetotalchargeineachofthepixeltothedigitalADUvalueforthatpixel.
Themosteffectivewaytoobtainaqualitybiasimageistoaverage10ormoresingle
biasframes.[7]
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3.3.2DarkFrames
Adarkframeisalsoanexposuretakenwiththeshutterbeingclosed.Thedark
framemeasurestheamountofthermalnoise,alsocalleddarkcurrent,foundonthe
CCDchipduringexposuretime.Thedarkframeshouldbeanexposurelastingthe
sameamountoftimeastherawimageframe.Anastronomerplanstotakea10‐
minuteexposureofanobject,shouldtakeadarkframlasting10minutes.Dark
framesalsoprovideinformationabout“hot”pixelsontheCCDchip.“Hot”pixels
readhigherthanaveragepixels.[7]
CCDSoftgivesuserstheoptionofautomaticallytakingadarkframepriortoan
imagingsessionandapplyingittoeachimage.Inmostsituations,thisdarkframe
willbesufficient,howevertherearecertaintypesofresearchthatrequireusersto
takeandapplythedarkframetoeachimage.
3.3.3Flat‐Fields
Aflat‐fieldimagecorrectsvariationsamongthethousandsofpixelslocatedon
anindividualCCDchip.Flat‐fieldframesareobtainedbytakinganopen‐shutter
Figure10:AmasterbiasframeusedtocalibrateimagestakenwiththeBYUICCDcamera.
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imageofauniformbackdrop.[7]Flat‐fieldcalibrationimagesaremuchmore
difficulttoobtainthanbiasordarkframes.Forthisreason,therearemanymethods
forobtainingaqualityflat‐field.Thetwomostcommonmethodsaredetailedbelow.
Onewaythatanyastronomercanobtainaflat‐fieldimageistoaimtheirtelescope
atthetwilightskywhenitisevenlyilluminated.Severalshotsshouldbetakenand
anaveragewillcreateaqualityflat‐field.ADUcountsshouldbeabouthalfofthefull‐
wellcapacity.
3.3.4MasterCalibrationImage
Onceeachcalibrationimageistaken,CCDSoftcancreateaMasterCalibration
Imagethatcanbeappliedtoanentiresetofimages.Thisisdonebyfollowingthe
stepslistedbelow:
1.Inthetoolbar,clickImage>>Reduce>>ImageReduction.
2.Select“AddGroup”andnametheimagereductiongroup.
3.Highlightthefolderlabeled“BiasFrames”andselect“AddFrames.”
Figure11:AmasterflatusedtocalibrateimagestakenwiththeBYUIdahoCCDcamera.
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4.Uploadeachofthebiasimagesthatweretakenforthatspecificsetofimages.
5.FollowthesameprocedureforFlatFramesandDarkFrames(ifapplicable).
Once each of these groups has been uploaded, CCDSoft provides an option to
combinetheimages;thiswillcreateaMasterBiasFrame,MasterDarkFrame,and
Master Flat Field. These frameswill be used to reduce the raw image in order to
reducethemajorityofunwantednoise. Imagereductionessentiallytakestheraw
image and subtracts the bias frames and dark frames and then divides the entire
imagebythemasterflatfield,yieldingafinalreducedobjectframe:
€
Final Object Frame =RawObject − BiasFrame −Dark Frame
Flat Field (2)
Whileimagecalibrationmaysounddifficultintheory,CCDsoftwarepackages,
suchasCCDSoftandMaximDL,maketheprocesssimpleandeffective.Image
calibrationeffectivelyincreasestheimagesSignal‐to‐NoiseRatio(S/N):
€
SN
=N *
N *+np(ns+ nd + nr2) (3)
WhereN*isthenumberofphotonscollectedduringobservationovertheentire
areaofinterest(canbeonepixelormany),npisthenumberofpixelsunder
consideration,nsisthenumberofphotonsperpixelduetobackgroundnoise,ndis
thenumberofdarkcurrentelectronsperpixel,andnristhenumberofelectrons
perpixelfromreadoutnoise.Thegoalofimagecalibrationistomaketheimage’s
S/Nratioashighaspossible,whichhappensasthens+nd+nr2termbecomessmall.
Thefinalproductofthisprocessisaqualityimagethatcanbeusedforscientific
analysis.[3]
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Figure12:ImageofM92priortocalibrationimagesbeingapplied.
Figure13:ImageofM92aftercalibrationimageshavebeenapplied.
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ChapterIV.Photometry
Inastronomy,photometryistheprocessofmeasuringthebrightnessofstarsin
thesky.[8]Photometricstudiesproveextremelyusefulforastronomersseekingto
determineluminosities,magnitudes,anddistancesofstarsandotherobjects.More
advancedtechniquescanyieldinformationaboutanobject’stemperatureor
chemicalmake‐up.Photometryisalsoemployedwhenstudyingvariablestars,
activegalacticnuclei,andsupernovae,aswellassearchingforminororextrasolar
planets.
CCDdevicesareidealforphotometricevaluationsbecausetheycandistinguish
smalldifferencesinbrightness.Theresearchoutlinedinthispaperisbasedonthe
useoftheSBIGST‐7XMEcamerainordertoobservetheperiodofthevariablestar
RVUrsaMajor.Whilevariablestarstudiescanbeeffectivelycompletedusingthe
BYU‐Idahotelescopeset‐up,therearealsomanyothertypesofprojectsthatwillbe
detailedlateron.
4.1VariableStars
Avariablestarisanystarwhosebrightnesschangesovertime.Thechangein
brightnesscanvaryfromafewhundredthsofamagnitudetoasmuchas10or15
magnitudes.Thetimescaleforthischangemightbeafewminutesorseveralyears.
Allofthesechangesandtimescalesdependonthetypeofvariablestarinquestion.
Severaldatabaseshavebeensetuptoorganizeandcatalogthemorethan100,000
variablestarsthathavebeenobservedbyprofessionalandamateurastronomers.
[9]
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DatabasesusedforthisprojectincludetheAAVSOonlinecatalog,andthe
GeneralCatalogueofVariableStars(GCVS)foundwithinTheSky6Professional
EditionAstronomySoftwarepackage.
Therearesixmaintypesofvariablestarsthatcanalsobeclassifiedintofurther
categories:
1.EruptiveVariableStars–EVSstarsreleaselargeamountsofenergysuddenly
thatcausethebrightnesstoincreasebyasmuchas200timeswithinashortperiod
oftime.Aviolentprocesssuchasstellarflarescausesthisenergyrelease.Variability
inanEVSstarcanbedifficulttotrackbecausethetimebetweeneruptionsis
random.
2.PulsatingVariableStars–PVSstarsexperienceperiodicexpansionand
contraction,similartolungrespirationinhumans.Theseperiodicchangesinsize
canbeuniformacrossthestarordistributedonlyonasingleside,dependingonthe
stabilityofthestar’ssurface.
3.CataclysmicVariableStars–CVSstarsexperienceoutburststhatarecausedby
intensethermonuclearprocesses.LargenovaeareanexampleofaCVS.Inmost
cases,CVSstarsareextremelyclosebinarysystems.
4.RotatingVariableStars–RVSstarsareirregularlyilluminatedandmaybe
brighterononesidethantheother,orhaveadistinctshapethatmakesoneside
appearbrighterthantheother.Whilethestar’sbrightnessdoesnotactuallychange,
itappearstovaryfromtheastronomer’spointofviewasthestarrotatesonitsaxis.
5.EclipsingBinaryStars–EBSstarsystemsaretwoormorestarsthatinteractin
suchawaythattheyperiodicallyeclipseoneanother,causingtheapparent
magnitudeofthesystemtochangewithrespecttotheobserver.
22
6.OpticallyVariableXRaySources–Thisdistincttypeofvariablestarcanonly
beobservedthroughtheuseofspecializedequipmentthatmonitorsthex‐rays
emittedfromagivenstellarobject.Theschooldoesnotcurrentlyhavecapabilities
toperformsuchresearch.[10]
RVUrsaMajor,thevariablestarstudiedthroughoutthisproject,isaspecifictype
ofpulsatingvariablestarknownasRRLyraestars.Morecommonly,RRLyrae
variablesareconsideredpartofaclassofvariablesknownasCepheids.
4.2ObservingVariableStars
Observingvariablestarsrequiressomepractice,butwiththerightequipmentit
canbedonesuccessfullyandaccurately.Manyofthestarsfoundindatabases
requireperiodicobservationsinordertoensureaccuracyandnoteanychangesin
theperiodorluminosityofthestar.Thesedatabasesprovidevarioustoolsthat
assistobserversinmakingaccuratemeasurements.Forinstance,theAmerican
AssociationofVariableStarObservers(AAVSO)providesstarchartsthatassistin
findingspecificvariablestars.Thesestarchartsalsoindicateallstandardstarsthat
arefoundwithinthefieldofviewofagiventelescope.Standardstarswillbe
discussedfurtherinsection4.3.
Oncethecoordinatesforthevariablestarhavebeenlocated,TheSky6can
automaticallypointthetelescopetothatstar.TheSkyalsocontainsalargedatabase
ofvariablestarsandtheirpositionsinthesky.
Dependingontheexpectedperiodofthevariablestar,imagesshouldbetakenat
distinctintervals.Iftheperiodofavariablestarisseveralmonthsoryears,oneor
twoimagesmightbeadequatepernight.However,iftheperiodisoverthecourseof
23
afewhoursordays,imagesshouldbetakenmorefrequently.CCDSoftcanmakethis
processeasybysimplybeingsetuptotakeanimageautomaticallyatagiventime
interval,allowingobserverstotakehundredsofimagesduringthecourseofthe
nightwithoutactuallybeingnearthetelescope.
4.3AperturePhotometryMeasurements
CCDshavemademeasuringtherelativemagnitudesofvariablestarssimple.
Onceasetofimageshasbeentaken,asophisticatedcomputerprogramfound
withinMaximDLcancreateasetofdatapointsthatcorrespondtotherelative
magnitudeofthevariablestarforeachimage.
MaximDLemploysatechniqueknownasaperturephotometry.Thesoftware
generatesanapertureoverthestarandaddsupeachoftheADUcountsforevery
pixelfoundwithintheaperture.Asimilarapertureisplacedoverthestandardstar
andthetotalnumberofcountsforeachstariscompared.Thisgivesaratioofthe
numberofphotoelectronsthatreachedtheCCDdevicefromonestaroverthe
numberofphotoelectronsfromthestandardstar.Theprogramalsotakesinto
accountanybackgroundnoisefoundthroughouttheimageinordertoensuremore
accurateresults.
Measuringtherelativemagnitudeofavariablestarrequiresknowledgeofthree
objectsineachimage:standardstars,checkstars,andthevariablestar.
1.StandardStars–Standardstarsareanessentialpartofvariablestarobservation.
Thesestarsareregularlymonitoredandhavebeenshowntonotvaryinbrightness.
Thisgivestheobserverawaytocomparethevariablestar’sbrightnesstoa
24
standardbrightness.Ifastar’sluminosityappearstochangewithrespecttothe
standardstarthenitisconsideredavariablestar.
Duringmeasurements,thestandardstarisassigneditsacceptedmagnitudein
eachoftheimages.Forexample,intheresultsfoundinAppendixBthestandard
starwasassignedamagnitudeof12.567.TheADUcountsofthecheckandvariable
starscanthenbecomparedtotheADUvalueofthestandardstarsandassigneda
magnituderelativetothestandardstar.
2.CheckStars–Thecheckstarisusedtocalculatetheuncertaintyintheimages.
Whenmorethanonestandardstarisfoundwithinthefieldofview,oneisassigned
tobethestandardstarwhiletheotheristhecheckstar.
Themagnitudeofthecheckstarisdeterminedbycomparingthenumberof
photoelectronswithinitsaperturetothenumberofphotoelectronsinthestandard
star’saperture.Becausethecheckstarisalsoastandardstar,ideallyitwillbe
measuredtohavethesamemagnitudeineveryimage.
Inlessthanidealsituations,themagnitudeofthecheckstarwillvaryfromimage
toimage.Thisvariationisduetoerrorsintheimagingprocess,atmospheric
turbulence,andotherimperfectionsinthemeasurementprocess.Thestandard
deviationofthecheckstarmagnitudesresultsinthestandarddeviationineachof
thestarsofthatimageandcanbereportedastheerrorinthevariablestar’s
magnitudecalculations.
AppendixBshowsthemeasurementsofthecheckstarmagnitudeineachofthe
imagesusedintheresearchofRVUrsaMajor.Thestandarddeviationofthecheck
starcanbefoundintheresultssectionofChapter5.
25
3.VariableStar–Thevariablestaristheobjectintheimagewhosemagnitude
changeswithtime.Theaperturethatisplacedaroundthevariablestaraddsupthe
totalnumberofphotoelectronsandcomparesthatnumbertothenumberof
photoelectronsfoundinthecheckstar.Arelativemagnitudeisthencalculatedand
assignedtothevariablestarforthatspecificimage.
Themagnitudeofthevariablestarisexpectedtochangeovertime,sothe
methodforcalculatingtheerrorinthevariablestaristoassignthesamestandard
deviationtothevariablestar’smagnitudeasthecheckstar’smagnitude.
InordertoaccessthephotometrytoolinMaximDL,usersshouldopenupallofthe
imagesintendedtobeanalyzedandfollowtheinstructionslistedbelow:
1.Inthetoolbars,selectAnalyze>>Photometry.
2.UndertheMouseclickTagsoption,select“NewObject.”
Figure14:Atypicalstarfieldwithindicatorsshowingthelocationsofthevariablestar,standardstar,andcheckstar.
26
3.Clickontheobjectthatisbeinganalyzed.ThepresetsettingsinMaximDLallow
theprogramtoautomaticallyselectthesameobjectineachoftheremainingimages
thatarebeinganalyzed,sothisonlyneedstobedoneinoneimage.
4.UndertheMouseclickTagsoption,select“NewReferenceStar.”
5.Clickontheregionwherethestandardstarisfoundintheimage.
6.Inputtheknownmagnitudeofthereferencestar.
7.UndertheMouseclickTagsoption,select“NewCheckstar”(ifapplicable).
8.Scanthrougheachoftheimagestoensurethatapertureshavebeenplaced
aroundeachoftheimportantobjects.Ifanimageisnothighqualityanddoesnot
includetheapertures,itcanbeexcludedbyselecting“ExcludeImage.”
9.Select“ViewPlot.”Thesoftwarewillanalyzeeachoftheimagesandafterafew
minuteswilluploadagraphshowingMagnitudealongthey‐axisandJulianDate
alongthex‐axis.
10.Select“SaveData.”MaximDLwillsavethedataasaCSVfilethatcanbeopened
inmostspreadsheetapplications,suchasMicrosoftExcel.
Figure15:AscreenshotoftheMaximDLPhotometrytoolinaction.Theaperturescanbeseenaroundthevariable,reference,andcheckstars.
27
Oncethedataisobtained,analysiscanbemadeandalightcurvecanbecreated.
Alightcurveindicatestheperiodofthevariablestar,alongwiththemaximumand
minimummagnitudes.Inordertoobtainaccuratemagnitudes,themagnitudeof
bothcheckandreferencestarsshouldbepreciselyknown.
Asisthecasewithallscientificstudies,variablestarstudieshaveamarginof
errorassociatedwiththem.Standardprocedureforerrorcalculationinvariablestar
studiesistocalculatethestandarddeviationofthemagnitudevaluesobtainedfor
thecheckstar.[11]MaximDLwillautomaticallyassignthedesignatedmagnitudeto
thereferencestarofeachimage.Thecheckstarwillthenvaryinaccordancewith
theerroroftheimage(SeeAppendixforcheckstarmagnitudevaluesandsample
errorcalculations).Anidealsituationwillreportthesamemagnitudeforthecheck
staroneachoftheimagestaken.Inmostcases,however,astandarddeviation
between0.01and0.1isobtained.Photometricstudiesthatresultinastandard
deviationlargerthan0.1isoftenconsideredtobetooerroneoustobeuseful.
28
ChapterV.RVUrsaMajorVariableStarStudy
Inthischapterwereportonthefindingsofaphotometricevaluationofthe
variablestarRVUrsaMajor.ThisstarislocatedintheUrsaMajorconstellationat
RightAscension13:33:18.09andDeclination+53:59:14.60(2000).Accordingtothe
AAVSO,thisstarhasaperiodof0.46806daysandhasreportedmaximum
magnitudesof9.8andminimummagnitudesof11.3.Astarchartoftheregioncan
befoundintheAppendix.
TheprimaryexpectationoftheresultsistoobtainaperiodoftheRVUrsaMajor
thatiscomparabletotheaccepted0.46806days.Themaximumandminimum
magnitudesarenotexpectedtobeobservedsimilarlytothoselistedbytheAAVSO,
mainlybecausethosearetheouterlimitsreportedtothedatabase,andmost
extremevaluesareonlyrecordedoccasionally.Wealsoexpecttobeabletocreatea
phasecurvedetailingtheperiodofRVUrsaMajorandtheshapeofitscurve.
Thereportedresultswereobtainedbetween8‐17‐2010and8‐27‐2010atthe
BYU‐Idaholivestockcenterusinga10”Maksutov‐Newtoniantelescopewithan
attachedSBIGST‐7XMEcamera.Theimagesweretakenusingthestandardclear
filteroftheSBIGCFW‐10filterwheel.
29
5.1Results
Figure16:Magnitudesfoundoveran11dayperiod.DataforthisfigurecanbefoundintheAppendix.Uncertaintyinmagnitudeovertheentirerangeofdataisfoundinthebottomcornerofthegraph.
ThedatarepresentedinFigure16isallofthedataobtainedduringthe11‐day
analysisofRVUrsaMajor.Itcanbenotedthatseveralmaximaandminimaare
foundinthedata.InordertodeterminetheaverageperiodofRVUrsaMajor,the
timedifferencebetweenthelastreportedmaximumandthefirstreported
maximumiscalculatedandthendividedbythetotalnumberofperiodsthatare
expectedduringthattime.Inthisstudy,thenumberofexpectedperiodsis
determinedbasedupontheacceptedperiodof0.46806days.Thefollowing
equationrepresentsthisrelationship,
€
(2455435.67131− 2455426.78939)days19periods
= 0.46746 days period (4)
andisalsoexpressedinTable1.
Table1:Thefirstandlastmaximaobservedoveran11dayperiodwiththeaverageperiodreportedasthetimedifferencedividedbytheexpectednumberofperiodsoverthegiventime.TheuncertaintycalculatedisbasedonastandarddeviationoftheaverageperiodsinTable2.
σ=0.03091
30
Iftheexpectednumberofperiodswereunknown,observerswouldneedto
acquiresufficientdatainordertodetermineanestimatedperiodfromachart
similartoFigure16.
Theuncertaintyintheperiodisalsodeterminedbyusingastandarddeviation,
similartotheuncertaintyinthemeasurementsofthemagnitude.Thedatausedto
determinetheerrorintheperiodarefoundinTable2.EachoftheJuliandateslisted
aremeasuredmaximaofRVUrsaMajorandtheDifference(JD)columnshowsthe
timedifferencebetweeneachmeasuredmaximum.Thecolumnlabeled“Numberof
Periods”istheexpectednumberofperiodsthathavepassedbetweenmaximabased
ontheacceptedperiodicityof0.46806days.TheAveragePeriodisthedifferencein
timebetweenperiodsdividedbythenumberofperiodsexpectedtohavepassed.
Table2:TheJulianDateofeachoftheobservedmaximaalongwiththeaverageperiodreportedbetweentheobservedmaxima.
Variablestardataisoftenreportedinaphasecurve.Phaseisaquantitybetween
0and1assignedtoeachimagethatdescribestheplaceintheperiodorvariationof
thevariablestar.DuetothelengthoftimeoftheperiodofRVUrsaMajor,itisnot
possibletorecordanentireperiod,orphase,ofthelightcurveoverthecourseof
onenight.Adifferenttechniquemustbeemployed.
Tocreatethestar’sphasecurve,asseeninFigure17,eachofthedatapoints
mustbeassignedtoagivenpartoftheperiod.Thiscanbedoneoncetheaverage
31
periodofthestarhasbeendetermined.Theelapsedtimefromtheinitialimageto
theimageinquestioncanbecalculatedandthendividedbytheaverageperiodof
thestar.Thetotalnumberofperiodsthathavepassedisthensubtractedfromthe
value,resultingineachimagebeingassignedavaluebetween0–1.
Figure17:PhasecurveofRVUrsaMajordetailingthegeneralshapeofthelightcurveofthevariablestar.
5.2AnalysisofResults
ThemeasuredperiodofRVUrsaMajorbetween8‐17‐2010and8‐27‐2010was
0.46746±0.00395days.Theacceptedvalueof0.46806iswithintherangeoferror
forthismeasurement.Themaximummagnitudemeasuredduringtheperiodof
observationwas10.350andtheminimummagnitudewas11.116.
ThephasecurveplotaccuratelydescribestheactivityofRVUrsaMajorand
correlateswellwithwhatmostCepheidvariablephasecurvesshow.Thestar
quicklyreachesitsmaximummagnitudeandslowlydimsforseveralhoursbefore
againdramaticallyincreasinginmagnitude.Itisnoted,however,thatmanymore
10.3
10.4
10.5
10.6
10.7
10.8
10.9
11.0
11.1
11.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mag
nitu
de
Phase
RV Ursa Major Phase Curve
32
datapointsvaryfromtheexpectedphasecurveduringthedimmestportionsofthe
periodcomparedtothoseatthebrightestportionsoftheperiod.Thisispossibly
duetoalargernaturalvariationinbrightnessduringthispartoftheperiod.
Themarginoferrorinthemagnitudemeasurementswas±0.03091forthe
entirerangeofdata.Thefirsttwodaysofmeasurementsweremuchlessaccurate
andcontributedprimarilytothisstandarddeviation.Themarginoferrorforthe
firsttwonightswas±0.05312.Moreaccuratefocusingresultedintheremaining
daysyieldingamarginoferrorof±0.02350.Theseresultsshowtheimportanceof
achievingaccuratefocuspriortoimaging.
FuturedataisexpectedtobemuchmoreaccurateduetotheassistanceofDr.
TomDavis.Dr.Davisisalocalexpertinamateurastronomyandassistedinproperly
collimatingandaligningthetelescope.Aproperlycollimatedtelescopecanyield
signal‐to‐noiseratiosthatare5ormoretimesashighasthoseachievedduringthis
project.
33
ChapterVI.ConclusionandFutureResearch
6.1Findings
Themainresearchgoalofthisprojectwastoanalyzeandunderstandthe
periodicityofthevariablestarRVUrsaMajor.Thevariablestarexhibitsfeaturesof
otherCepheidvariablestars.Thestarhasashortperiodof0.46746±0.00395days
anditslightcurveissimilartootherperiodicandCepheidvariablestars.
6.2FutureResearch
Asidefromthevariablestarstudy,thisprojectwasintendedtoguidefuture
researchbyBYU‐Istudents.StudentsatBYU‐Idahowhohavelittleornoprevious
experienceinastronomycanobtainresearchexperienceatthetelescopesight.The
followingisalistofseveralofthemanypossibleprojectsthatcouldbeperformed
bystudents:
1.VariableStarStudies–Thereareliterallyhundredsofthousandsofvariable
starsintheskythatmustbemonitoredandreportedtogroupssuchasAAVSO.
Additionalinformationandalistofresourcescanbefoundatwww.aavso.org.
2.Spectroscopy–Whiletheschooldoesnotcurrentlyhaveaccesstothe
instrumentsneededtoanalyzethespectroscopyofstellarobjects,itisapossibility
inthefutureforinterestedstudents.Varioustypesoffilterscanbepurchasedwhich
allowobserverstorecordtheamountofhydrogen,helium,andotherelements
foundwithinanobjectandthusdetermineitsstructure.
34
3.MinorPlanetandCometSearches–TheBYU‐Idahotelescopecurrentlyhasthe
capabilitiestosearchforandmonitorminorplanetsinourownsolarsystemaswell
asdiscoveringandmonitoringcomets,asteroids,andotherorbitingobjects.
4.DataAnalysis,ImageCombiningandReductionTechniques–Inorderto
obtainthemostaccurateresultsandproducethehighestqualityimagespossible,
projectscouldbeperformedtodeterminethemosteffectivewaytoreduce,
combine,andanalyzeimages.Thesetypesofprojectswouldgreatlybenefitfuture
studentsandguidefutureresearch.
Manyresourcesarefoundoncampusrangingfromlibrarybooksand
seniorpapers,tofacultymemberswithpriorexperience.Iffuturestudentstake
initiativeanddesiretoproducequalityresearchwiththeBYU‐Idahotelescope,
theywillhaveanopportunitytogainresearchskillsandcontributetoreal
science.
35
Bibliography
[1]MichaelA.Covington,AstrophotographyfortheAmateur,2ndEd.,CambridgeUniversityPress(2001).[2]MichaelW.Davidson,AnatomyofaChargeCoupledDevice,http://micro.magnet.fsu.edu/primer/digitalimaging/concepts/ccdanatomy.html,accessed9/18/2010.[3]SteveB.Howell,HandbookofCCDAstronomy,CambridgeUniversityPress(2000).[4]CameronJones,AstrophotographyUsingtheBrighamYoungUniversityIdahoMakNewtTelescope,(2010).[5]SantaBarbaraInstrumentGroup,SoftwareBisque,Inc.,CCDSoftUser’sGuide,Version5,(2006).[6]SoftwareBisque,Inc.,TheSky6AstronomySoftwareUser’sGuide,Revision1.0.0.10,(2006).[7]S.Parimucha,M.Vanko,PhotometryoftheVariableStarsUsingCCDDetectors,AstronomicalInstituteoftheSlovakAcademyofSciences,(2005).[8]AmericanAssociationofVariableStarObservers,TheAAVSOCCDObservingManual,(2009).[9]M.Saldyga,Variables:WhatAreTheyandWhyObserveThem?,AmericanAssociationofVariableStarObservers,http://www.aavso.org/variables‐what‐are‐they‐and‐why‐observe‐them,accessed9/24/2010.[10]GerryA.Good,ObservingVariableStars,1stEd.,SpringerPublishing(2003).[11]MichaelKoppelman,UncertaintyAnalysisinPhotometricObservations,SocietyforAstronomicalSciences.Accessedthroughhttp://articles.adsabs.harvard.edu//full/2005SASS...24..107K/0000107.000.html,(2005).
36
AppendixA—RVUrsaMajorStarChart
ThestarchartlocatedonthispagewasprovidedcourtesyoftheAmerican
AssociationofVariableStarObservers.Theorganizationwassetupinorderto
provideassistancetoamateurastronomersacrosstheworld.Numbersindicate
standardstarswhoseknownmagnitudesarealsolistedonthewebsite.
37
AppendixB—Data
Julian Date RV Ursa Major
Magnitude Standard
Star Check Star
2455426.66953 11.130 12.567 7.893 2455426.67168 11.120 12.567 7.888 2455426.67384 11.104 12.567 7.896 2455426.67604 11.061 12.567 7.903 2455426.67816 11.069 12.567 7.852 2455426.68028 11.051 12.567 7.838 2455426.68240 11.058 12.567 7.854 2455426.68451 10.963 12.567 7.813 2455426.68663 11.020 12.567 7.854 2455426.68875 11.057 12.567 7.904 2455426.69099 11.039 12.567 7.869 2455426.69321 11.050 12.567 7.916 2455426.69532 11.077 12.567 7.936 2455426.69744 11.039 12.567 7.901 2455426.69956 11.023 12.567 7.921 2455426.70168 11.017 12.567 7.900 2455426.70380 11.089 12.567 7.961 2455426.70592 10.998 12.567 7.881 2455426.70804 11.008 12.567 7.902 2455426.71016 11.056 12.567 7.943 2455426.71228 10.993 12.567 7.908 2455426.71441 11.016 12.567 7.945 2455426.71652 10.964 12.567 7.886 2455426.71864 10.912 12.567 7.793 2455426.72077 10.958 12.567 7.858 2455426.72289 11.010 12.567 7.923 2455426.72501 10.947 12.567 7.905 2455426.72713 10.953 12.567 7.901 2455426.72925 11.002 12.567 7.934 2455426.73137 10.844 12.567 7.839 2455426.73349 10.927 12.567 7.938 2455426.73560 10.883 12.567 7.905 2455426.73772 10.911 12.567 7.945 2455426.73984 10.860 12.567 7.937 2455426.74196 10.826 12.567 7.897 2455426.74408 10.781 12.567 7.934 2455426.74620 10.770 12.567 7.912 2455426.74832 10.729 12.567 7.886 2455426.75044 10.721 12.567 7.918 2455426.75256 10.609 12.567 7.868 2455426.75468 10.535 12.567 7.809 2455426.76675 10.403 12.567 7.887 2455426.76887 10.342 12.567 7.871 2455426.77100 10.360 12.567 7.868 2455426.77312 10.324 12.567 7.904 2455426.77525 10.287 12.567 7.865 2455426.77738 10.335 12.567 7.875 2455426.77950 10.318 12.567 7.890 2455426.78162 10.335 12.567 7.904 2455426.78375 10.327 12.567 7.890 2455426.78588 10.344 12.567 7.894 2455426.78800 10.324 12.567 7.877 2455426.78939 10.273 12.567 7.835 2455426.79194 10.347 12.567 7.861 2455426.79406 10.330 12.567 7.860 2455426.79618 10.326 12.567 7.862 2455426.79832 10.332 12.567 7.845 2455426.80045 10.396 12.567 7.901 2455426.80256 10.337 12.567 7.837 2455426.80468 10.380 12.567 7.850 2455426.80681 10.388 12.567 7.866 2455426.80894 10.413 12.567 7.890 2455426.81125 10.406 12.567 7.864 2455426.81365 10.407 12.567 7.834
2455426.81578 10.414 12.567 7.848 2455426.81791 10.420 12.567 7.864
2455426.82003 10.451 12.567 7.882 2455426.82216 10.441 12.567 7.838 2455426.82429 10.433 12.567 7.815 2455426.82641 10.475 12.567 7.847 2455426.82854 10.426 12.567 7.843 2455426.83067 10.493 12.567 7.854 2455426.83280 10.504 12.567 7.844 2455426.83493 10.508 12.567 7.824 2455426.83706 10.485 12.567 7.854 2455426.83918 10.515 12.567 7.832 2455426.84131 10.525 12.567 7.893 2455426.84344 10.496 12.567 7.816 2455426.84556 10.554 12.567 7.869 2455426.89411 10.682 12.567 7.903 2455426.91963 10.839 12.567 7.898 2455426.92663 10.789 12.567 7.901 2455427.66935 10.858 12.567 7.870 2455427.67162 10.841 12.567 7.918 2455427.67375 10.871 12.567 7.900 2455427.67587 10.799 12.567 7.914 2455427.67799 10.767 12.567 7.919 2455427.68011 10.746 12.567 7.935 2455427.68223 10.707 12.567 7.876 2455427.68435 10.674 12.567 7.894 2455427.68647 10.569 12.567 7.876 2455427.68859 10.559 12.567 7.933 2455427.69072 10.516 12.567 7.925 2455427.69284 10.533 12.567 7.910 2455427.69496 10.490 12.567 7.917 2455427.69709 10.420 12.567 7.903 2455427.69921 10.416 12.567 7.903 2455427.70133 10.415 12.567 7.873 2455427.70345 10.338 12.567 7.873 2455427.70558 10.350 12.567 7.891 2455427.70769 10.384 12.567 7.911 2455427.70981 10.318 12.567 7.912 2455427.71193 10.255 12.567 7.880 2455427.71405 10.284 12.567 7.887 2455427.72041 10.329 12.567 7.908 2455427.72253 10.340 12.567 7.894 2455427.73101 10.394 12.567 7.891 2455427.73313 10.354 12.567 7.887 2455427.73525 10.414 12.567 7.916 2455427.73737 10.297 12.567 7.865 2455427.73970 10.277 12.567 7.888 2455427.74183 10.280 12.567 7.910 2455427.74820 10.280 12.567 7.875 2455427.76308 10.388 12.567 7.968 2455427.76520 10.436 12.567 7.876 2455427.76733 10.485 12.567 8.057 2455427.76945 10.473 12.567 7.823 2455427.77158 10.500 12.567 7.774 2455427.77371 10.474 12.567 7.771 2455427.77796 10.454 12.567 7.691 2455427.78008 10.542 12.567 7.770 2455427.78221 10.521 12.567 7.806 2455427.78433 10.570 12.567 7.839 2455427.78645 10.527 12.567 7.860 2455427.78858 10.550 12.567 7.865 2455427.79070 10.552 12.567 7.823 2455427.79282 10.574 12.567 7.835 2455427.79494 10.601 12.567 7.851 2455427.79960 10.612 12.567 7.694 2455427.80200 10.620 12.567 7.869 2455427.80413 10.590 12.567 7.827 2455427.80626 10.631 12.567 7.864 2455427.80838 10.636 12.567 7.875 2455427.81050 10.624 12.567 7.883 2455427.81263 10.687 12.567 7.902
38
2455427.81475 10.695 12.567 7.871 2455427.81688 10.689 12.567 7.839 2455427.81901 10.659 12.567 7.766 2455427.82114 10.626 12.567 7.834 2455429.64685 10.534 12.567 7.826 2455429.64970 10.561 12.567 7.921 2455429.65182 10.560 12.567 7.794 2455429.65379 10.565 12.567 7.878 2455429.65699 10.590 12.567 7.998 2455429.65910 10.590 12.567 7.867 2455429.66122 10.596 12.567 7.604 2455429.66334 10.595 12.567 11.971 2455429.66546 10.608 12.567 11.975 2455429.66758 10.620 12.567 11.968 2455429.66970 10.626 12.567 11.952 2455429.67182 10.629 12.567 11.974 2455429.67394 10.649 12.567 11.960 2455429.67606 10.653 12.567 11.958 2455429.67818 10.654 12.567 11.958 2455429.68030 10.655 12.567 11.962 2455429.68242 10.668 12.567 11.954 2455429.68454 10.669 12.567 11.946 2455429.68666 10.674 12.567 11.950 2455429.68878 10.683 12.567 11.957 2455429.69090 10.709 12.567 11.960 2455429.69302 10.689 12.567 11.961 2455429.69514 10.705 12.567 11.957 2455429.69726 10.724 12.567 11.959 2455429.69938 10.725 12.567 11.955 2455429.70150 10.717 12.567 11.966 2455429.70362 10.739 12.567 11.963 2455429.70574 10.744 12.567 11.964 2455429.70786 10.749 12.567 11.942 2455429.70998 10.754 12.567 11.950 2455429.71209 10.765 12.567 11.970 2455429.71421 10.757 12.567 11.959 2455429.71633 10.762 12.567 11.943 2455429.71845 10.782 12.567 11.964 2455429.72057 10.784 12.567 11.964 2455429.72269 10.785 12.567 11.956 2455429.72481 10.800 12.567 11.962 2455429.72693 10.816 12.567 11.951 2455429.72905 10.804 12.567 11.941 2455429.73117 10.809 12.567 11.954 2455429.73329 10.820 12.567 11.960 2455429.73541 10.817 12.567 11.955 2455429.73753 10.837 12.567 11.936 2455429.73965 10.839 12.567 11.956 2455429.74177 10.858 12.567 11.963 2455429.74389 10.853 12.567 11.953 2455429.74601 10.855 12.567 11.948 2455429.74813 10.864 12.567 11.954 2455429.75024 10.886 12.567 11.953 2455429.75236 10.883 12.567 11.942 2455429.75434 10.891 12.567 11.950 2455429.75789 10.887 12.567 11.973 2455429.76001 10.918 12.567 11.973 2455429.76213 10.894 12.567 11.964 2455429.76426 10.898 12.567 11.964 2455429.76638 10.919 12.567 11.978 2455429.76851 10.930 12.567 11.961 2455429.77064 10.927 12.567 11.949 2455429.77276 10.938 12.567 11.947 2455429.77488 10.944 12.567 11.963 2455429.77700 10.947 12.567 11.944 2455429.77912 10.963 12.567 11.948 2455429.78124 10.943 12.567 11.959 2455429.78336 10.962 12.567 11.970 2455429.78548 10.978 12.567 11.953 2455429.78760 10.966 12.567 11.958 2455429.78971 10.978 12.567 11.963 2455429.79183 10.971 12.567 11.948
2455429.79395 11.000 12.567 11.968 2455429.79607 10.983 12.567 11.970 2455429.79819 10.985 12.567 11.959 2455429.80031 10.986 12.567 11.958 2455429.80230 10.994 12.567 11.948 2455429.80654 11.009 12.567 11.940 2455429.80866 11.007 12.567 11.948 2455429.81078 11.022 12.567 11.965 2455429.81290 11.018 12.567 11.945 2455429.81502 11.009 12.567 11.939 2455429.81714 11.010 12.567 11.967 2455429.81926 11.009 12.567 11.933 2455429.82138 11.037 12.567 11.950 2455429.82350 11.005 12.567 11.966 2455429.82562 11.041 12.567 11.950 2455429.82774 11.045 12.567 11.951 2455429.82986 11.043 12.567 11.944 2455429.83198 11.029 12.567 11.948 2455429.83410 11.022 12.567 11.934 2455429.83623 11.032 12.567 11.965 2455429.83875 11.022 12.567 11.935 2455429.84439 11.006 12.567 11.965 2455429.84721 11.034 12.567 11.957 2455429.85003 11.022 12.567 11.951 2455429.85284 11.052 12.567 11.947 2455429.85566 11.038 12.567 11.933 2455429.85847 11.046 12.567 11.938 2455429.86129 11.020 12.567 11.917 2455429.86411 11.047 12.567 11.942 2455429.86693 11.053 12.567 11.944 2455429.87255 11.046 12.567 11.921 2455429.87537 11.055 12.567 11.939 2455429.87819 11.072 12.567 11.928 2455429.88102 11.059 12.567 11.935 2455429.88384 11.055 12.567 11.929 2455429.88665 11.069 12.567 11.938 2455429.88947 11.060 12.567 11.942 2455429.89228 11.043 12.567 11.936 2455429.89510 11.032 12.567 11.938 2455432.64385 11.039 12.567 11.917 2455432.64804 11.042 12.567 11.916 2455432.65298 11.037 12.567 11.935 2455432.65649 11.042 12.567 11.898 2455432.66001 11.040 12.567 11.939 2455432.66352 11.053 12.567 11.916 2455432.66703 11.055 12.567 11.914 2455432.67054 11.057 12.567 11.986 2455432.67424 11.061 12.567 11.973 2455432.67883 11.077 12.567 11.970 2455432.68234 11.053 12.567 11.975 2455432.68585 11.049 12.567 11.973 2455432.68936 11.082 12.567 11.973 2455432.69287 11.067 12.567 11.976 2455432.69637 11.067 12.567 11.976 2455432.70053 11.063 12.567 11.981 2455432.70479 11.050 12.567 11.996 2455432.70830 11.056 12.567 11.969 2455432.71181 11.060 12.567 11.963 2455432.71532 11.068 12.567 11.987 2455432.71883 11.074 12.567 11.980 2455432.72234 11.070 12.567 11.969 2455432.72585 11.063 12.567 11.984 2455432.72937 11.073 12.567 11.965 2455432.73288 11.078 12.567 11.971 2455432.73640 11.065 12.567 11.972 2455432.73991 11.082 12.567 11.976 2455432.74343 11.081 12.567 11.987 2455432.74695 11.099 12.567 11.974 2455432.75046 11.101 12.567 11.962 2455432.75397 11.053 12.567 11.981 2455432.75748 11.082 12.567 11.970 2455432.76100 11.053 12.567 11.954
39
2455432.76451 11.056 12.567 11.968 2455432.76802 11.017 12.567 11.951 2455432.77154 11.048 12.567 11.988 2455432.77506 11.028 12.567 11.977 2455432.77859 11.004 12.567 11.943 2455432.78210 11.004 12.567 11.970 2455432.78548 10.983 12.567 11.957 2455432.79007 10.961 12.567 11.954 2455432.79358 10.949 12.567 11.949 2455432.79709 10.939 12.567 11.985 2455432.80060 10.935 12.567 11.973 2455432.80411 10.929 12.567 11.959 2455432.80762 10.896 12.567 11.983 2455432.81112 10.853 12.567 11.963 2455432.81463 10.879 12.567 11.962 2455432.81814 10.834 12.567 11.947 2455432.82165 10.791 12.567 11.950 2455432.82517 10.770 12.567 11.953 2455432.82868 10.730 12.567 11.952 2455432.83219 10.674 12.567 11.953 2455432.83570 10.630 12.567 11.934 2455432.83921 10.594 12.567 11.971 2455432.84272 10.545 12.567 11.922 2455432.84623 10.513 12.567 11.925 2455432.84975 10.437 12.567 11.935 2455432.85326 10.459 12.567 11.963 2455432.85678 10.410 12.567 11.937 2455432.86029 10.398 12.567 11.909 2455432.86380 10.397 12.567 11.956 2455432.86730 10.423 12.567 11.945 2455432.87081 10.406 12.567 11.947 2455432.87432 10.393 12.567 11.929 2455432.87783 10.366 12.567 11.955 2455432.88135 10.421 12.567 11.931 2455432.88487 10.409 12.567 11.938 2455432.88838 10.403 12.567 11.927 2455432.89223 10.456 12.567 11.941 2455432.89717 10.453 12.567 11.956 2455432.90069 10.488 12.567 11.964 2455432.90420 10.481 12.567 11.907 2455432.90771 10.515 12.567 11.920 2455432.91123 10.540 12.567 11.923 2455432.91474 10.550 12.567 11.903 2455432.91826 10.538 12.567 11.900 2455433.66602 11.075 12.567 11.920 2455433.67026 11.078 12.567 11.949 2455433.67376 11.068 12.567 11.940 2455433.67695 11.096 12.567 11.953 2455433.68188 11.093 12.567 11.925 2455433.68539 11.102 12.567 11.903 2455433.68890 11.097 12.567 11.922 2455433.69241 11.116 12.567 11.965 2455433.69592 11.085 12.567 11.967 2455433.69943 11.083 12.567 11.958 2455433.70293 11.076 12.567 11.979 2455433.70644 11.077 12.567 11.961 2455433.71040 11.047 12.567 11.971 2455433.71498 11.031 12.567 11.973 2455433.71849 11.021 12.567 11.993 2455433.72200 11.000 12.567 11.976 2455433.73690 10.963 12.567 11.975 2455433.74204 10.928 12.567 11.973 2455433.74663 10.886 12.567 11.983 2455433.75014 10.873 12.567 11.972 2455433.75365 10.824 12.567 11.970 2455433.75716 10.829 12.567 11.958 2455433.76067 10.761 12.567 11.959 2455433.76418 10.705 12.567 11.964 2455433.76769 10.687 12.567 11.972 2455433.77120 10.634 12.567 11.975 2455433.77514 10.543 12.567 11.979 2455433.77938 10.526 12.567 11.959
2455433.78289 10.453 12.567 11.993 2455433.78640 10.438 12.567 11.966 2455433.78991 10.430 12.567 11.960 2455433.79342 10.402 12.567 11.966 2455433.79692 10.377 12.567 11.969 2455433.80043 10.350 12.567 11.935 2455433.80394 10.355 12.567 11.980 2455433.80744 10.383 12.567 11.962 2455433.81095 10.408 12.567 11.968 2455433.81446 10.427 12.567 11.962 2455433.81797 10.404 12.567 11.988 2455433.82147 10.436 12.567 11.961 2455433.82498 10.431 12.567 11.958 2455433.82849 10.455 12.567 11.939 2455433.83200 10.487 12.567 11.942 2455433.83550 10.487 12.567 11.999 2455433.83901 10.477 12.567 11.985 2455433.84252 10.509 12.567 11.960 2455433.84603 10.506 12.567 11.981 2455433.84953 10.552 12.567 11.989 2455433.85304 10.542 12.567 11.956 2455433.85655 10.552 12.567 11.992 2455433.85990 10.553 12.567 11.998 2455433.86449 10.537 12.567 11.914 2455433.86800 10.589 12.567 11.945 2455433.87151 10.585 12.567 11.956 2455433.87502 10.595 12.567 11.999 2455433.87852 10.615 12.567 11.946 2455433.88203 10.658 12.567 11.965 2455433.88554 10.642 12.567 11.921 2455433.88905 10.659 12.567 11.901 2455433.89650 10.669 12.567 11.966 2455433.90144 10.677 12.567 11.929 2455433.90496 10.696 12.567 11.923 2455433.90847 10.672 12.567 11.917 2455433.91199 10.712 12.567 11.951 2455433.91550 10.720 12.567 11.951 2455433.91901 10.752 12.567 11.924 2455434.64951 11.021 12.567 11.941 2455434.65236 10.994 12.567 11.922 2455434.65448 10.986 12.567 11.911 2455434.65660 10.988 12.567 11.873 2455434.65872 10.985 12.567 11.930 2455434.66084 10.991 12.567 11.916 2455434.66295 10.960 12.567 11.926 2455434.66507 10.951 12.567 11.989 2455434.66719 10.954 12.567 11.980 2455434.66931 10.930 12.567 11.978 2455434.67143 10.921 12.567 11.989 2455434.67355 10.926 12.567 11.993 2455434.67567 10.911 12.567 12.002 2455434.67779 10.884 12.567 11.986 2455434.67991 10.889 12.567 11.985 2455434.68203 10.870 12.567 11.992 2455434.68414 10.851 12.567 11.975 2455434.68616 10.837 12.567 11.983 2455434.68936 10.798 12.567 11.995 2455434.69148 10.795 12.567 12.013 2455434.69360 10.770 12.567 11.974 2455434.69572 10.748 12.567 11.997 2455434.69784 10.733 12.567 11.989 2455434.69996 10.684 12.567 11.985 2455434.70207 10.683 12.567 11.991 2455434.70419 10.647 12.567 11.989 2455434.70631 10.599 12.567 11.992 2455434.70845 10.606 12.567 11.991 2455434.71057 10.557 12.567 11.991 2455434.71268 10.515 12.567 11.971 2455434.71480 10.529 12.567 11.978 2455434.71692 10.503 12.567 11.987 2455434.71904 10.477 12.567 11.974 2455434.72116 10.467 12.567 11.963
40
2455434.72328 10.432 12.567 11.994 2455434.72540 10.419 12.567 11.984 2455434.72753 10.376 12.567 11.980 2455434.72965 10.386 12.567 11.985 2455434.73176 10.399 12.567 11.991 2455434.73388 10.400 12.567 11.991 2455434.73600 10.379 12.567 11.979 2455434.73812 10.387 12.567 11.990 2455434.74024 10.391 12.567 11.978 2455434.74236 10.398 12.567 11.974 2455434.74448 10.395 12.567 11.969 2455434.74660 10.413 12.567 11.990 2455434.74872 10.417 12.567 11.986 2455434.75084 10.413 12.567 11.976 2455434.75296 10.407 12.567 11.976 2455434.75508 10.431 12.567 11.990 2455434.75719 10.419 12.567 11.980 2455434.75931 10.451 12.567 11.981 2455434.76143 10.439 12.567 11.973 2455434.76370 10.446 12.567 11.993 2455434.76582 10.469 12.567 11.966 2455434.76793 10.471 12.567 11.990 2455434.77005 10.475 12.567 11.993 2455434.77217 10.491 12.567 11.974 2455434.77429 10.491 12.567 11.995 2455434.77641 10.490 12.567 11.985 2455434.77853 10.503 12.567 11.971 2455434.78065 10.525 12.567 11.981 2455434.78277 10.529 12.567 11.983 2455434.78471 10.520 12.567 11.982 2455434.78860 10.535 12.567 11.978 2455434.79072 10.540 12.567 11.987 2455434.79284 10.550 12.567 11.968 2455434.79496 10.567 12.567 11.994 2455434.79708 10.563 12.567 11.999 2455434.79920 10.574 12.567 11.999 2455434.80132 10.574 12.567 11.975 2455434.80343 10.585 12.567 11.969 2455434.80555 10.583 12.567 11.968 2455434.80767 10.616 12.567 11.981 2455434.80979 10.594 12.567 11.981 2455434.81191 10.607 12.567 11.971 2455434.81403 10.606 12.567 11.973 2455434.81615 10.614 12.567 11.968 2455434.81835 10.634 12.567 11.985 2455434.82329 10.642 12.567 11.965 2455434.82575 10.641 12.567 11.975 2455434.82823 10.654 12.567 11.960 2455434.83071 10.638 12.567 11.980 2455434.83318 10.680 12.567 11.962 2455434.83564 10.644 12.567 11.964 2455434.83811 10.660 12.567 11.976 2455434.84058 10.683 12.567 11.952 2455434.84304 10.700 12.567 11.954 2455434.84551 10.662 12.567 11.949 2455434.84798 10.687 12.567 11.949 2455434.85044 10.692 12.567 11.965 2455434.85291 10.726 12.567 11.942 2455434.85538 10.754 12.567 11.951 2455434.85785 10.730 12.567 11.953 2455434.86033 10.729 12.567 11.959 2455434.86279 10.741 12.567 11.932 2455434.86526 10.748 12.567 11.913 2455434.86773 10.738 12.567 11.929 2455434.87021 10.760 12.567 11.943 2455434.87267 10.761 12.567 11.969 2455434.87514 10.786 12.567 11.922 2455434.87761 10.775 12.567 11.940 2455434.88007 10.784 12.567 11.962 2455434.88255 10.782 12.567 11.952 2455434.88502 10.791 12.567 11.917 2455434.88749 10.803 12.567 11.927
2455434.88997 10.814 12.567 11.906 2455434.89243 10.852 12.567 11.950 2455434.89491 10.830 12.567 11.922 2455434.89738 10.815 12.567 11.945 2455434.89986 10.820 12.567 11.924 2455434.90233 10.859 12.567 11.929 2455434.90481 10.846 12.567 11.901 2455434.90728 10.886 12.567 11.917 2455434.90976 10.835 12.567 11.935 2455434.91224 10.868 12.567 11.943 2455434.91471 10.913 12.567 11.894 2455435.64947 10.564 12.567 11.889 2455435.65723 10.473 12.567 11.943 2455435.66075 10.429 12.567 11.923 2455435.66427 10.424 12.567 11.936 2455435.66780 10.411 12.567 11.910 2455435.67131 10.383 12.567 11.904 2455435.67483 10.392 12.567 11.951 2455435.67834 10.398 12.567 11.978 2455435.68185 10.398 12.567 11.985 2455435.68536 10.401 12.567 11.963 2455435.68888 10.410 12.567 11.991 2455435.69239 10.416 12.567 11.986 2455435.69591 10.439 12.567 11.957 2455435.69943 10.451 12.567 11.964 2455435.70294 10.476 12.567 11.975 2455435.70645 10.462 12.567 11.997 2455435.70997 10.487 12.567 11.917 2455435.71348 10.490 12.567 11.962 2455435.71700 10.530 12.567 11.943 2455435.72051 10.539 12.567 11.961 2455435.72404 10.530 12.567 11.967 2455435.72862 10.539 12.567 11.982 2455435.73213 10.546 12.567 11.956 2455435.73564 10.567 12.567 11.967 2455435.73915 10.593 12.567 11.983 2455435.74266 10.610 12.567 11.974 2455435.74616 10.591 12.567 11.966 2455435.74967 10.604 12.567 11.932 2455436.73050 10.740 12.567 11.978 2455436.73931 10.744 12.567 11.952 2455436.75294 10.795 12.567 11.951 2455436.75649 10.836 12.567 11.972 2455436.75930 10.823 12.567 11.968 2455436.76212 10.852 12.567 11.947 2455436.76495 10.843 12.567 11.942 2455436.76776 10.867 12.567 11.976 2455436.77058 10.851 12.567 11.945 2455436.77340 10.857 12.567 11.978 2455436.77622 10.861 12.567 11.944 2455436.77871 10.897 12.567 11.980 2455436.78297 10.870 12.567 11.945 2455436.78578 10.914 12.567 11.986 2455436.78860 10.898 12.567 11.965 2455436.79141 10.903 12.567 12.000 2455436.79423 10.888 12.567 11.959 2455436.79705 10.926 12.567 11.980 2455436.79987 10.934 12.567 11.951 2455436.80270 10.942 12.567 11.976 2455436.80552 10.940 12.567 11.956 2455436.80834 10.982 12.567 11.973 2455436.81116 10.924 12.567 11.954 2455436.81398 10.943 12.567 11.947 2455436.81680 10.956 12.567 11.951 2455436.81962 10.964 12.567 11.981 2455436.82245 10.972 12.567 11.975 2455436.82527 10.995 12.567 11.985 2455436.82778 10.990 12.567 11.958 2455436.83272 10.973 12.567 11.981 2455436.83554 10.974 12.567 11.922 2455436.83835 10.970 12.567 11.939 2455436.84117 10.975 12.567 11.967
41
2455436.84398 11.001 12.567 11.949 2455436.84681 11.002 12.567 11.948 2455436.84964 10.986 12.567 11.972 2455436.85245 11.019 12.567 11.974 2455436.85527 11.009 12.567 11.952 2455436.85794 10.997 12.567 11.948 2455436.86374 10.990 12.567 11.960 2455436.86673 10.999 12.567 11.945 2455436.86972 11.002 12.567 11.940 2455436.87271 11.005 12.567 11.962 2455436.87570 11.013 12.567 11.935 2455436.87870 11.003 12.567 11.955 2455436.88169 11.022 12.567 11.951 2455436.88468 11.035 12.567 11.942 2455436.88767 11.005 12.567 11.933 2455436.89067 11.014 12.567 11.946 2455436.89366 11.013 12.567 11.945
2455436.89664 11.036 12.567 11.937 2455436.89963 11.009 12.567 11.950 2455436.90262 11.065 12.567 11.930 2455436.90561 11.028 12.567 11.933 2455436.90860 11.029 12.567 11.963 2455436.91160 11.022 12.567 11.921 2455436.91459 11.000 12.567 11.921 2455436.91757 11.017 12.567 11.915 2455436.92056 11.006 12.567 11.945 2455436.92356 11.011 12.567 11.914 2455436.92654 11.045 12.567 11.953 2455436.92953 11.057 12.567 11.913 2455436.93252 11.068 12.567 11.908 2455436.93552 11.026 12.567 11.913 2455436.93851 11.092 12.567 11.889
42
AppendixC—CalculatingUncertainty
Mostofthesourcescitedinthisreportgivedetailedinstructionson
calculatingtheuncertaintyofthefindings.Thissectionsummarizesthemost
basicmethodforcalculatingerror.Moreintensiveprojectsmayrequire
additionalmethodstobeappliedinordertodeterminetheuncertainty.
Researchersarereferredtosourcescitedinthistext,specificallyKoppelman.
[11]
Themostbasicmethodforcalculatinguncertaintyistodeterminethe
standarddeviationofthecheckstarmagnitudes.Thestandarddeviationis
definedas,
€
σ =1N
(xi − xi=1
N
∑ )2 (5)
whereNisthenumberofsamples,xiisthemagnitudeofthecheckstarforthe
imageinquestion,and
€
x istheaveragevalueforallofthecheckstarmagnitudes
inquestion.
Forexample,giventhefollowingdatawhichispartiallytakenfromactual
datausedinthisreport,
Julian Date RV Ursa Major Magnitude
Standard Star
Check Star
2455426.66952657 11.130 12.567 7.893 2455426.67168105 11.120 12.567 7.888 2455426.67383925 11.104 12.567 7.896 2455426.67604185 11.061 12.567 7.903 2455426.67815936 11.069 12.567 7.852 2455426.68027687 11.051 12.567 7.838 2455426.68239658 11.058 12.567 7.854 2455426.68451457 10.963 12.567 7.813 2455426.68663219 11.020 12.567 7.854
thestandarddeviationwouldbecalculatedtobe0.03074.Theonlyvaluesthat
areconsideredarethecheckstarmagnitudes.Fromthiscalculationitcaneasily
beseenthatthelargerthesamplesize,themoreaccuratethestandarddeviation
willbeindeterminingtheuncertaintyofthedataset.
43
AppendixD—TelescopeSet‐upSteps
1. Uncovertelescope.2. AttachDewShield.3. Attach9‐PinKeyspancabletoRS‐232serialportandUSBendtocomputer.4. SecurelyattachCCDCameratotelescopeeyepiece.5. ConnectpowersupplytoCCDcamera.6. ConnectAutoguidingcabletotheCCDcameraandtheGTDControlPanel.7. ConnectCCDUSBfromthecameratothecomputer.8. OpeneitherMaximDL4orCCDSoft.Note:Theseinstructionsaredirected
morespecificallytoCCDSoftusers.MaximDLuserswillfindthatthecommandsaresomewhatsimilar.
9. ConnecttheCCDdevicetothecomputer.10. Setthedevice’stemperature.11. Connecttelescope’spowersupply.12. ConnectAstro‐PhysicshandcontrollertotheGTDControlPanel.13. Select“Location1”andthen“ResumeRef‐Park1”.14. OpenTheSky6ProfessionalEdition.15. Establishthelinkbetweenthecomputerandthetelescope.16. Checktomakesurethecomputer’sclockissetcorrectlyandthatTheSkyis
usingthecomputer’sclock.17. Setviewingorientation.18. Syncthetelescopetoabrightobjectthatiseastofthemeridian.Seesection
2.2.3inResearchUsingBYUITelescopeandPhotometryofVariableStarRVUrsaMajor.
19. FocustheCCDdevice.20. Takecalibrationimages.Note:BiasImagescanbetakenanytime;darkframes
shouldbetakenjustpriororjustafterimagingsession,orboth;flatfieldswillgenerallybetakenwhenduringtwilighthourswhentheskyismostevenlyilluminated.
21. Pointtelescopeatstellarobjecttobeimaged.22. Setuptheauto‐guidingfeature.23. Setimagetime,numberofimagestobetaken,filtertobeused,andanyother
preferencesdesiredfortheimage.24. Beginimaging.25. Saveimage.Note:Autosavingisafeatureavailablethatwillautomatically
saveallimagestakenwhileenabled.26. Whenfinishedimaging,turnofftemperaturecontrolandallowtheCCD
devicetocooldownforseveralminutes.27. ReturntelescopetoParkPosition1.28. Turnoffpowersupplies,unplugallcablesandstoretheminasafeplace.29. RemoveDewShieldandplaceblacklidbackonthetelescope.30. RemoveCCDdeviceandreplacewhitecoverovertheeyepiece.31. Covertelescopesecurelywithtarpsprovided.
44
