Ver. 032601AST 1002 Slide Handouts: Topic G Page 1Copyright © 2001 H.L. CohenDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C1Topic GTopic GBinary Stars (Stellar Twins)(Web Version: 03-26-01)Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C2Binary Stars &The Mass-Luminosity RelationCorrelation in ScienceDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C3Overview of Binary StarsVery abbreviated . . .• Definition• Importance• Frequency• Stellar Masses (Mass-Luminosity Relation)• Stellar DensitiesVery BriefDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C4Binary Stars§ Definition• Orbiting stars bound by gravitationJust like planets and Sun!u Importance• Common (over 50% of stars)• Source of fundamental info (especially mass)u Interesting!• Some so close nearly touch!Become distorted & facing sides heatDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C5Double Stars: Two TypesEarth Near Star Far StarSee ThisBut could be either . . .Optical DoubleEarth A Binary SystemPhysical DoubleA “Double Star”Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C6Double Stars: Two TypesHow Tell?(Binaries)Thought could find near star’s parallax using far star as reference!Most Physical– Why?– Too many doubles to be just “chance”• Later confirmation– Orbital motion observed(Periods sometimes hundreds of years)• William Herschel (English: 1738–1822)– Guessed most optical– Later changed mind!Ver. 032601AST 1002 Slide Handouts: Topic G Page 2Copyright © 2001 H.L. CohenDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C7The Early Case for BinariesExample . . . considerCastor (αα Geminorum)5"AB(Separation about 5 arc sec)Could this be chance (optical double)?A. Brighter (1.9 mag.)B. Fainter (2.9 mag.)Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C8Analogy§ Take . . .How many grains of wheat do you expectto lie within 1/2 inch of each kernel of corn?§ Scatter corn & wheat over a ten acre field!(Amounts reflect relative numbers of stars for each magnitude)• 50 corn kernels (analogous to component A)A• 400 wheat grains (analogous to component B)BDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C9What Do You Think?50 kernels400 grainsTen AcresNot very many (1 in 300,000)!But suppose you found dozens . . .what would you conclude?Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C10Likewise . . .§ Find thousands of doubleswith components too closeto be all chance§ That is, can’t all be optical§ Many must be physical!(i.e., binary stars)ABDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C11Frequency of Binary Stars*Examples of Bright Binary StarsSirius . . . . . . . . . . . . . . . . . . . BrightestPolaris . . . . . . . . . . . . . . . . . North StarAlpha Centauri . . . . . . . . . . . ClosestCapella (6th brightest) . . . . . One of 1st knownMizar (in Big Dipper) . . . . . . Naked eyeAlbireo (head of Cygnus) . . . Spectacular!*Some are really multiple (e.g., Castor is six!)SeeStudy GuideTopic F Question #34Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C12Test Your Eye Sight“Naked Eye Double”• Find Big Dipper• Look at 2nd star from handle’s endBig DipperLittle DipperPolaris MizarAlcorWant Big Dipper high so …Fall: Look in morningSpring: Look in eveningTry it!Mizar (mag . +2.3)Alcor (mag . +4.0)(Separation 12 arc min)Ver. 032601AST 1002 Slide Handouts: Topic G Page 3Copyright © 2001 H.L. CohenDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C13Can’t Split Mizar?Big DipperLittle DipperPolaris MizarAlcorMizarAlcorUse Binoculars!(Easily “splits”!)12'Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C14Look With Small TelescopeBig DipperLittle DipperPolaris MizarAlcorMizar splits into components A & B!MizarAlcor15" apartABSpectroscopy also shows A & Beach binaries!Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C15Nearest StarsFor the eight stars nearest Earth (within 10 ly) § One possibly single§ Five binaries§ One triple§ One planetary systemQuestion — Which one has planets?Answer — ?Binary star surveys suggest most stars multiple orhave planets!Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C16How Stellar Masses Found§ Recall mass measured by gravitational effects• Need two close masses• Binary stars ideal§ Question:What principal used to determine mass?§ Answer: Newton’s version of Harmonic Law(M + m) P 2= a 3(review!)Calculate From ObservationsDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C17Individual Stellar Masses• Note: (M + m) P 2= a 3gives sum of masses!(not each mass)• Suggestion: Do #13(Topic G) in Study Guide• Mass Ratio ( M / m ): If also known, can find M & m (see #14)• Simple Example: M + m = 4 and M / m = 3 / 1– Find M and m ?– Answer M = 3 and m = 1 !Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C18Results§ Range of stellar masses small• Most 1/10 to 10 solar masses• 10 to 50 solar masses uncommon(only for the rare O & B stars)§ Main sequence stars show a“mass–luminosity relation”See Table 13See Fig. 16Ver. 032601AST 1002 Slide Handouts: Topic G Page 4Copyright © 2001 H.L. CohenDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C1930 20 3 2 1 0.75 0.5-50+5+10Absolute MagnitudeMass (Sun = 1)The Mass-Luminosity RelationSunEarly Main Sequence StarsLate Main Sequence StarsHigh MassLow MassNotice small range of mass Main Sequence Stars Only(Stars not on main sequence donot show this relation)See Fig. 16(Mass = 1)Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. C20Fig. 13. The HR DiagramYou can alsoput this resultinto yourHR DiagramFig. 13in Study GuideDept. Astronomy – University of Florida – Copyright © H.L. Cohen 1997, Ver. 04139762OOBBAAFFGGKKMM-5-500+5+5+10+10Absolute MagnitudeAbsolute MagnitudeThe HR DiagramThe HR DiagramSunSunEarly Main Sequence StarsEarly Main Sequence StarsLate Main