Introduc)on to Astrophysics. Unit 5: Stars

Transcription

1 Introduc)on to Astrophysics Unit 5: Stars 1

2 Plan Stars are Suns so start by learning what we can about our local star To compare to other stars, need to find luminosity, temperature, size, and mass Combine sta)s)cs with stellar models to understand how stars work 2

3 The Sun Shines but How? Sun is big and hot so luminous L How does it stay hot? M = kg Chemical (rearrange electrons - electromagne)c) burning produces J per atom, or J per kg. Need to burn kg/s so run out in 10 4 y Kelvin- Helmholtz (gravita)onal) energy would last 10 7 y = W 3

4 Nuclear Physics Why don t nuclei break up under electric repulsion? A strong arrac)ve force binds nucleons Short- range since atoms do not collapse m 4

5 Nuclear Energy Rearranging nucleons recover nuclear energy In large nuclei distant nucleons barely arract Breaking up fission or emission recover electromagne)c energy Heats planets powers reactors 5

6 In small nuclei, less arrac)ve interac)ons Liberate nuclear energy by fusion to Helium Problem: Hydrogen is all protons Strong interac)ons cannot change a proton to a neutron Fusion? 6

7 Weak Interac)ons Something can do this! And the inverse A free neutron decays in 15min n! p + + e + e Weak nuclear force mediates this decay 7

8 Some Ques)ons and Answers Can a force change one par)cle into another? Yes Is a neutron just a )ny Hydrogen atom? No What is e? Are there any rules? Conserva)on Laws Mass- Energy Momentum Angular Momentum Electric Charge Electron Number E = mc 2 Weak interac)on: rare 8

9 9 Par)cle Q N e p n e e p n e + e Par)cle Physics An)par)cle: same mass opposite charges Neutrinos almost massless, weakly interac)ng Discovered as missing energy in n decay

10 Solar Energy p- p chain is source of Solar Energy p + + p +! d + + e + + e d + + p +! 3 He 2+ 3 He He 2+! 4 He 2+ + p + + p + 4p +! 2+ +2e + +2 e J Sun could last y 10

11 What it Takes To ini)ate fusion, protons must overcome electric repulsion One proton must inverse decay before highly unstable 2 He breaks up Requires temperatures of 10 6 K - only in core Inefficient because weak process required 11

12 How Do We Know? Theory (Eddington, Bethe 1932) first Davis, Bahcall (1968): Detect the e Pro: Penetrate Sun Con: Penetrate detector Flux at Earth: e m 2 s Put a tank with of Chlorine in Homestake Gold Mine 380 m 3 37 Cl + e! 37 Ar + e Requires high- energy e produced in other processes Expect one atom per six days 12

13 Where Are the Neutrinos? Flux Found is less than predic)ons Is Solar Model wrong? Is detector model wrong? Decided in 2001 by SNO: par)cle physics 13

14 More Par)cles, More Charges Par)cle Q N e N μ N τ Mass p n e e µ µ ? ? ? 14

15 So What? Neutrinos change spontaneously en route pp process produces When they arrive, 1/3 are This implies, in par)cular, that neutrinos are not massless although light. e e 15

16 Studying the Sun Solar models together with helioseismology provide interior structure between core and photosphere Density, pressure, temperature increase with depth for hydrosta)c equlibrium 16

17 Core: Solar Structure - Core R apple.25r K T K kg/m kg/m 3 M 0.4M Stable equilibrium: fusion rate decreases/increases: core contracts/expands increasing/decreasing rate Luminosity determined by mass 17

18 Solar Structure Inner Mantle Radia)on Zone:.25R apple R apple.7r K T K kg/m kg/m 3 Heat transfer: Radia)on diffusion in charged plasma Transit )me: y 18

19 Solar Structure Outer Mantle Convec)on Zone:.7R apple R apple R K T 5780 K 10 3 kg/m kg/m 3 Heat Transfer: Convec)on produces granular structure of photosphere 19

20 Solar Atmosphere Sun extends beyond photosphere Density low but temperature increases with al)tude Chromosphere: h apple 2000 km 5780 K apple T apple 50, 000 K kg/m kg/m 3 Observe by line H 20

21 Corona: 2000 km apple h apple 1.3 R T K kg/m 3 Visible during Eclipse or with coronagraph Observed in UV, X- Ray High temperature allows escape: Solar wind Corona 21

22 Blemishes First recorded Gan De 364BC Galileo used them to find rota)on period 25.4d Dark because cooler 4000K Wilson 1769: depressions in photosphere 22

23 PaRerns Sunspot number varies in 11y cycle Sunspot pairs appear first at mid- la)tudes and later near equator Spots are regions of increased magne)c field choking convec)on Pair polarity consistent in hemisphere/cycle reverses between cycles 23

24 Solar Magne)sm Solar field not simple dipole Differen)al rota)on of charged plasma deforms field in convec)on zone High fields at surface produce reconnec)on events Reconnec)on releases energy in field, reverses polarity every 11y 24

25 Magne)c Storms Reconnec)on releases magne)c energy accelera)ng charged par)cles Sudden release of up to J in flare heats gas to 10 7 K More violent: Prominences, Coronal Mass Ejec)ons Cause geomagne)c storms 25

26 Stars in 3d - Parallax To measure distance to star measure change in its apparent posi)on as seen from different points. Measure this rela)ve to more distant stars Most distant observatories: same place, different seasons D 1AU = p D 1pc = 1 p 26

27 First Steps on the Ladder First stellar parallax measured by Bessel 1838 ShaRers celes)al sphere extends 3d to stars What s an AU? Best measurement: radar telemetry to planets. This determines pc Hipparchos 1989 measures 120,000 stars, leading to current catalog of 2,500,000 Gaia 2013 will vastly extend this 27

28 28

29 Proper Mo)on Some nearby stars observed to move rela)ve to distant stars Find tangen)al velocity v T from angular proper mo)on µ v T =4.74µD Radial velocity from Doppler v r = c( / 0 1) 29

30 30 Big Dipper?

31 If We Know the Distance Can measure brightness and compute 2 luminosity L =4 D 2 b Measure color (spectrum) to find temperature Compare the two to find radius 31 R = L 4 T 4 L L T = m K 1/2 max R R = = b b L L D 1AU 1/2 T T 2

32 A BeRer Thermometer Blackbody spectrum too broad and subject to distor)on by medium Stellar line spectra give berer data Atmosphere composi)on and ioniza)on state indicate temperature 32

33 33 Spectral Lines and Temps

34 Type Color Temperature Lines Prevalence Examples O Blue > 33,000 He 0, He +, weak H < % Orion s Belt B Blue- White 10,000-33,000 He 0, strong H.13% Spica,Rigel A White to Blue- White ,000 No He, Very strong H, some metal ions F White strong H, many metal ions G Yellowish White Weak H, many metals.6% Sirius, Vega 3% Procyon,Polaris 7.6% Sun, Capella K Orange Neutral metals 12.1% Arcturus, Aldebaran M Red Neutral Metals, molecular bands 76.5% Betelgeuse 34

35 Stellar Sta)s)cs We can now use all this to study proper)es of stars as a popula)on Luminosity varies hugely Radius varies less PaRerns appear when you arrange it right: Herzsprung- Russell

36 Luminosity Classes How to tell an orange giant from a much smaller orange MS star? Morgan, Keenan, Kellerman 1943: Spectral lines for small stars show effects of higher pressure, density Sun s spectral class is G2V 36

37 Spectroscopic Parallax From spectrum can obtain spectral class Extract luminosity from H- R diagram Use brightness to find distance No parallax D 1AU = s L L b b 37

38 An Example: Alphecca Dim white star. Flux Spectrum classifies it as A0V Luminosity from HR Radius: R CB = L CB L 1/2 T CB T b CB = b L CB = 74L 2 R T CB = 9700K = p =3R

39 Distance: D CB = Hipparchos: s 10% error typical Alphecca L CB L b b CB AU = p 74/ = AU = 25.7pc p CB = D CB = 22.9pc 39

40 Partners About 1/5 of all stars are gravita)onally bound to a partner Glossary: Visual: can see both Op)cal Double: not binary Non- visual: other methods α- Centauri AB is a triple with Proxima Centauri 40

41 α- Centauri is Famous As nearest star to Earth this has been of interest to many October, 2012: an Earth- sized planet detected orbi)ng α- Centauri B at 0.04 AU 41

42 Star posi)on gives a projec)on of orbit on tangent plane Can find radial component by Doppler shiy Get complete orbit With Benefits Given period and radius find mass M 1 + M 2 M = 3 2 R P 1AU 1y Plozng mo)on of both partners find M 1 R 1 = M 2 R 2 R 1,R 2 42

43 Spectroscopic Binaries If stars too close to resolve can dis)nguish periodic Doppler shiy: Spectroscopic Binary If we can see both stars: double- line binary Oyen see only one 43

44 Measure: Learning from Spectrum v 1,v 2,P v = c ( / 0 1) R 1,2 = v 1,2P M 1 R 1 = M 2 R 2 M 1 v 1 = M 2 v 2 2 M = M 1 + M 2 = M 1 (1 + v 1 /v 2 )=M 1 (v 2 + v 1 )v 2 R = R 1 + R 2 = Pv Pv 1 2 =(v 1 + v 2 ) P 2 44

45 P 2 = 4 2 GM R3 Finding Masses R = P 2 (v 1 + v 2 ) M = 4 2 R 3 GP 2 = 4 2 P 3 (2 ) 3 GP 2 (v 1 + v 2 ) 3 M =(v 1 + v 2 )M 1 /v 2 M 1 = v 2P 2 G (v 1 + v 2 ) 2 We can find masses! M 1 = P 1y Caveat: Orbit may )lt, we measure only If we only see one star only know v 1 v 2 (v 1 + v 2 ) 2 (29.78km/s) 3 M v r 45

46 Eclipsing Binaries As with planets binaries in which one star transits the other provide more informa)on Light curve tells us about period, sizes, and temperatures Observing Doppler shiys and light curve get more complete data 46

47 Alphecca Alphecca is a double- line eclipsing binary with P = d Doppler measurements yield Predict: M 1 = P 1y v 2 (v 1 + v 2 ) 2 (29.78km/s) 3 M = M 2 = v 1 /v 2 M 1 =1.1M v 2 = m/s v 1 = m/s =3.2M 47

48 How Did We Do? Spectrum agrees: αcb B is G5V Light Curve data refine this (eccentricity 0.37) Best Fit: 48 Property 1 2 M/M R/R T (K) L/L

49 Mass Sta)s)cs Add mass for main sequence to our plot Masses vary lirle Model: Stars are the same: mass determines rest Heavy stars hot, luminous 49

50 Mass- Luminosity Rela)on Find approximately L L = M M 3.5 Borne out by models: Mass compresses star increasing rate of fusion If amount of Hydrogen available for fusion is near constant frac)on, big stars run out sooner OB stars are young! 50

51 Basics Stellar modeling matched to data tells us about how stars work Main- Sequence stars fuse Hydrogen to Helium in core Hydrosta)c Equilibrium determines rate of fusion and density profile from mass 51

52 In large stars M>1.5M core hot and CNO chain dominates fusion Rate rises rapidly with temperature CNO Chain 52

53 Size MaRers Mechanisms of heat transfer depend on mass In small stars, en)re volume convec)ve so all available to fuse in core In large stars, radia)on and convec)on zones inverted 53

54 Expansion by Contrac)on As a main sequence star ages core enriched in Helium Rate of fusion decreases temperature and radia)on pressure decrease Number of par)cles decreases thermodynamic pressure decreases Core contracts and heats Fusing region grows Luminosity increases Envelope expands Sun now 25% brighter than when it formed Core now 60% Helium Con)nues to brighten hea)ng Earth In 1-3Gy could be uninhabitable? Orbit stable out to 1Gy? 54

55 Summary For 90% of stars we have a good understanding of how they work This comes from careful observa)on and detailed modeling Where do the rest come from? What happens when core is all Helium?? 55