Ver. 081501AST 1002 Slide Handouts: Topic H: Part 3 Page 1Copyright © 2001 H.L. CohenDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 0815011Topic HTopic H“Part 3: A Solar Model”(Web Version: 08-15-01)Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 0815012Step 3. Baking InstructionsAnalogous to solution of all equations for all unknown stellar propertiesCalculations very tedious . . . so“Oven” = Fast,large memory,computer!, .Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 0815013Step 3. How Complex?§ For each stellar layer (shell) have• Four basic equations• Probably several “auxiliary equations”§ Total unknowns =No. Equations x No. of Shells Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 0815014Example§ Suppose have• 7 stellar equations for 7 unknowns• Make 100 layers (shells) in star§ Total number of unknowns to find is7 x 100 or 700 !Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 0815015Some Results1) How star’s thermostat works(i.e., gravity vs. gas pressure)2) Star’s internal structure3) Star’s chemical compositionDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 0815016Supposehappenstance makes T dropslightly**e.g., H diminishesH-Burning ThermostatE = Energy Production RateT = TemperatureP = Gas PressureCon = Core ContractionExp = Core ExpansionT downE PConTEPExpdowndownupupupCon/Exp?Con/Exp?(On Web: Fig. 23)Ver. 081501AST 1002 Slide Handouts: Topic H: Part 3 Page 2Copyright © 2001 H.L. CohenDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 0815017Results From A Stellar Model See Study GuideFigure. 17 Two Graph SummaryalsoFigure. 18 Pictorial ModelDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 0815018A Solar Model0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Fraction from Center40%20%0%60%80%100%PropertyMassTemperatureDensityLuminosityCenter Halfway Out SurfaceDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 0815019Mass0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.040%20%0%60%80%100%Fraction from CenterMassMass40% of mass within 20% of center!Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150110Density0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.040%20%0%60%80%100%Fraction from CenterDensity(Average Density only 1.4 gm/cc)160 gm/cc(Pressure = 330 billion Earth atmospheres!)Density32 gm/cc within 20% of centerDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150111Temperature0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.040%20%0%60%80%100%Fraction from CenterTemperature16 million K6,000 K(H Burning minimal below 10 million K)Temperature10 million KDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150112Luminosity0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.040%20%0%60%80%100%Fraction from CenterLuminosity95%Luminosity95% of luminosity within 20% of center!Not surprising since only core:(1) Dense enough & (2) hot enough for H burningVer. 081501AST 1002 Slide Handouts: Topic H: Part 3 Page 3Copyright © 2001 H.L. CohenDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150113A Pictorial Solar Model*40% of MassWithinInner 20%Nearly allH Burningtakes placein coreCore6,000 K(Surface)16,000,000 KCentralTemperature*See Study Guide Figure 18Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150114Energy Transport In SunCoreSo energy moves out from coreby radiationRadiativeZoneGas “transparent”to short waveradiation hereDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150115CoreOuter Zone ConvectiveFun Fact: Radiation takes about 30 million years to get out!• Gas opaque to radiation here• Energy moves by circulation of gasesRadiativeZoneConvective(mixing zone)Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150116Movie: Solar Granulation• Bright = hot, rising • Dark = cooler, descending10,000 kmCred. Neal Hurburt, Lockheed Palo Alto Research Labs.Size of EarthDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150117ConclusionsCore and surface layers do not mix !(1) Hydrogen on surface can’t move into core!• So not available for fuel• But no problem—most hydrogen in center!(2) Helium made in core can’t move to surface!Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150118The Solar CompositionCoreSurfaceH 70%He 28%Metals 2%“Original” (Zero Age) SunCoreH 70%He 28%Metals 2%SameHomogeneousCompositionSee Fig. 18, BottomVer. 081501AST 1002 Slide Handouts: Topic H: Part 3 Page 4Copyright © 2001 H.L. CohenDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150119The Solar CompositionSurfaceH 70%He 28%Metals 2%CoreHHeMetalsPresent Sun: Age 5 Billion YearsCore2%35%63%Metals remain unchanged50% of H lost (becomes He)35% new He adds to originalConsequence: 50% Through H-BurningH-Burning Lifetime: 10 Billion Years (see Table 17, Col. 4)See Fig. 18, BottomDept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150120No Mixing between core and surfaceCoreRadiativeZoneConvective• Core becomes H poor & He rich.• Why doesn’t surface also show this?• Ans. Sun mostly radiative (core & surface don’t easily mix)QuestionSurfaceH 70%He 28%Metals 2%CoreH 35%He 63%Metals 2%Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150121• Where does solarmodel fall?Solar ModelTLObserved Main SequenceSolar ModelSun’s model falls onmain sequence!Sun• Use predicted L & T to plot into HR Diagram• Answer:Onmain sequence!Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150122• Get a familyStellar FamiliesTLObserved Main SequenceAll models fall onmain sequence!• Keep composition same but change mass• Answer:All onmain sequence!SunAll Stellar Models• Where domodels fall?Dept. Astronomy – University of Florida – Copyright © H.L. Cohen 2001, Ver. 08150123So, Main Sequence is . . .1. A H-burning zone2. Of different mass stars3. With similar initial compositions4. All in hydrostatic