Lecture Outline Chapter 11: Our Star © 2015 Pearson Education, Inc. Why does the Sun shine? © 2015 Pearson Education, Inc. Is it on FIRE? … NO! Chemical Energy Content ~ 10,000 years Luminosity © 2015 Pearson Education, Inc. Is it CONTRACTING? … NO! Gravitational Potential Energy ~ 25 million years Luminosity © 2015 Pearson Education, Inc. E = mc2 —Einstein, 1905 It is powered by NUCLEAR ENERGY! Nuclear Potential Energy (core) ~ 10 billion years Luminosity © 2015 Pearson Education, Inc. Gravitational equilibrium: Gravity pulling in balances pressure pushing out. © 2015 Pearson Education, Inc. Energy balance: Thermal energy released by fusion in core balances radiative energy lost from surface. © 2015 Pearson Education, Inc. Gravitational contraction… provided energy that heated the core as the Sun was forming. Contraction stopped when fusion started replacing the energy radiated into space. © 2015 Pearson Education, Inc. What is the Sun's structure? © 2015 Pearson Education, Inc. 11.2 Nuclear Fusion in the Sun Our goals for learning: • How does nuclear fusion occur in the Sun? • How does the energy from fusion get out of the Sun? • How do we know what is happening inside the Sun? © 2015 Pearson Education, Inc. Fission Fusion Big nucleus splits into Small nuclei stick together smaller pieces. to make a bigger one. (Nuclear power plants) (Sun, stars) © 2015 Pearson Education, Inc. High temperatures enable nuclear fusion to happen in the core. © 2015 Pearson Education, Inc. The Sun releases energy by fusing four hydrogen nuclei into one helium nucleus. © 2015 Pearson Education, Inc. IN 4 protons OUT 4He nucleus 2 gamma rays 2 positrons 2 neutrinos Total mass is 0.7% lower. © 2015 Pearson Education, Inc. Thought Question What would happen inside the Sun if a slight rise in core temperature led to a rapid rise in fusion energy? A. The core would expand and heat up slightly. B. The core would expand and cool. C. The Sun would blow up like a hydrogen bomb. Solar thermostat keeps the rate of fusion steady. © 2015 Pearson Education, Inc. Solar Thermostat Decline in core temperature Rise in core temperature causes fusion rate to drop, causes fusion rate to rise, so core contracts and heats so core expands and cools up. down. © 2015 Pearson Education, Inc. Energy gradually leaks out of the radiation zone in the form of randomly bouncing photons. © 2015 Pearson Education, Inc. Convection (rising hot gas) takes energy to the surface. © 2015 Pearson Education, Inc. Why does the Sun shine? • Because it is burning. • Because of its chemical energy. • Because of its gravitational energy. • Because of nuclear fusion. • Because of nuclear fission. © 2015 Pearson Education, Inc. Why is the Sun very dense on the inside? • Denser materials sank to the center. • Pressure of the overlying gas keeps the density high. • It formed from dense material. • Nuclear fusion increases the density in the core by changing hydrogen into helium. © 2015 Pearson Education, Inc. What conditions are required for nuclear fusion of hydrogen to occur? • A temperature of millions of degrees • High density • The presence of uranium • All of the above • A and B © 2015 Pearson Education, Inc. Neutrinos created during fusion fly directly through the Sun. Observations of these solar neutrinos can tell us what's happening in the core. © 2015 Pearson Education, Inc. Solar neutrino problem: Early searches for solar neutrinos failed to find the predicted number. More recent observations find the right number of neutrinos, but some have changed form. © 2015 Pearson Education, Inc. What causes solar activity? © 2015 Pearson Education, Inc. Sunspots… Are cooler than other parts of the Sun's surface (4000 K). Are regions with strong magnetic fields. © 2015 Pearson Education, Inc. Lecture Outline Chapter 12: Surveying the Stars How do we measure stellar luminosities? Thought Question These two stars have about the same luminosity— which one appears brighter? A. Alpha Centauri B. The Sun The relationship between apparent brightness and luminosity depends on distance: Luminosity Brightness (or “Flux”) = 4π (distance)2 L F = 4πd 2 We can determine a stars luminosity if we can measure its distance and apparent brightness: Luminosity = 4π(distance)2 ✕ (brightness) L = 4πd 2F Thought Question How would the apparent brightness of Alpha Centauri change if it were three times farther away? A. It would be only 1/3 as bright. B. It would be only 1/6 as bright. C. It would be only 1/9 as bright. D. It would be three times as bright. Parallax is the apparent shift in position of a nearby object against a background of more distant objects. Introduction to Parallax Parallax,(Distance(and(angular(size( d=#distance#;#p#=(parallax(angle( 1 d((in(“parsecs”)(=( p (in arcseconds) physical size (in AU) angular size (in arcsec) = distance (in parsecs) a s / AU = arcsec d / pc Clicker(quesNon( If a star has a measured parallax of p=0.1 arcsec, its distance, in parsec (pc), is: A. 0.1(pc( B. 1(pc( C. 0.01(pc( D. 10#pc# E. (100(pc( © 2015 Pearson Education, Inc. Clicker(quesNon( Two stars in a binary system are observed to be separated by an angle a = 1 arcsec. If the system has a measured parallax p=0.1 arcsec, the physical separation s between the stars is: A. 0.1(AU( B. 1(AU( C. 0.01(AU( D. 10#AU# E. (100(AU( ProperNes(of(Thermal(RadiaNon( 1. HoUer(objects(emit(more(light(per(unit(area(at(all( 4 frequencies:((((B/Bsun=(T/Tsun) # 2. HoUer(objects(emit(photons(with(a(higher(average(energy:((((((((((( λmax =500 nm (Tsun/T) Luminosity L & apparent brightness B • Luminosity: L = B 4πR2 = σT4 4πR2 4 2 – or: L/Lsun= (T/Tsun) (R/Rsun) – T= surface temperature – R= stellar radius • App. Brightness (“Flux) = F = L/4πd2 – d = distance 106 K Level of ionization also 5 10 K Ionized reveals a star's Gas temperature. 104 K (Plasma) 103 K Neutral Gas 102 K Molecules 10 K Solid Lines in a star's spectrum correspond to a spectral type that reveals its temperature: (Hottest) O B A F G K M (Coolest) Thought(QuesNon( Which(of(the(stars(below(is(hoUest?( A. M(star( B. F(star( C. A#star# D. K(star( What have we learned? • How do we measure stellar luminosities? – If we measure a stars apparent brightness and distance, we can compute its luminosity with the inverse square law for light. – Parallax tells us distances to the nearest stars. • How do we measure stellar temperatures? – A stars color and spectral type both reflect its temperature. Organizing(stellar(properNes:( The(HertzsprungDRussel((HDR)(diagram( An(HDR(diagram( plots(stars(by( their(luminosi6es( &(temperatures.( Luminosity Temperature BRIGHT HOT COOL FAINT Most stars fall somewhere on the main sequence of the H-R diagram. Stars with lower T and higher L than main- sequence stars must have larger radii. These stars are called giants and supergiants. Stars with higher T and lower L than main- sequence stars must have smaller radii. These stars are called white dwarfs. Which star is the hottest? A Luminosity Luminosity Temperature Which star is the most luminous? C Lumiosity Lumiosity Temperature Which star is a main- sequence star? D Luminosity Luminosity Temperature Which star has the largest radius? C Luminosity Luminosity Temperature Binary(Star(Orbits( Orbit(of(a(binary(star(system(depends(on(the( strength(of(gravity.((( ( This(allows(us(to(use(binary(observaNons(to(infer( stellar(masses!( Types(of(Binary(Star(Systems(( • Visual(binary( • Eclipsing(binary( • Spectroscopic(binary( About#half#of#all#stars#are#in#binary#systems.# Visual(Binary(( We(can(directly(observe(the(orbital(moNons(of( these(stars.( Eclipsing(Binary( We(can(measure(periodic(eclipses.( Spectroscopic(Binary( We(determine(the(orbit(by(measuring(Doppler( shigs.( Using(binaries(to(determine(mass( 3 M1 + M 2 (a / AU) = 2 M sun (P / yr) But since orbital speed V=2πa/P, we can also write 3 M1 + M 2 ⎛ V ⎞ P = ⎜ ⎟ M sun ⎝ Ve ⎠ yr where earth’s orbital speed is Ve = 2πAU/yr = 30 km/s. Main7sequence+stars+are( fusing(hydrogen(into( helium(in(their(cores,(like( the(Sun.( ( Luminous(mainDsequence( stars(are(hot((blue).( ( Less(luminous(ones(are( cooler((yellow(or(red).( High-mass stars Mass( measurements(of( mainDsequence( stars(show(that(the( hot,(blue(stars(are( much(more(massive( than(the(cool,(red( Low-mass stars ones.( Stellar(ProperNes(Review( Luminosity:+from(brightness(and(distance( ( D4 6 (0.08MSun)(10 LSun(–(10 LSun((100MSun)( ( Temperature:+from(color(and(spectral(type( ( (0.08MSun)(3000(K(–(50,000(K((100MSun)( ( Mass:+from(period((p)(and(average(separaNon((a)(of(binaryDstar( orbit( ( 0.08MSun(–(100MSun( MainDSequence(Star(Summary( HighDmass:( High(luminosity( ShortDlived( Large(radius( Blue (( ( LowDmass:( Low(luminosity( LongDlived( Small(radius( Red( © 2015 Pearson Education, Inc. Mass$and$Life@me$ Un&l#core#hydrogen# (10%#of#total)#is# #used#up# Sun's+life+expectancy:+10$billion$years$ $ Life+expectancy+of+a+10MSun+star:+ + $10$@mes$as$much$fuel,$uses$it$103$@mes$as$fast$ $ $100$million$years$~$10$billion$years$×$10/103$ $ Main$sequence$life@me$ t M / M M / M ms = sun ≈ sun t L / L 3 sun sun (M / M sun ) 2 ⎛ M sun ⎞ t = 10 Byr ms ⎝⎜ M ⎠⎟ When main sequence stars run out of H to fuse in their core, they become giants and supergiants. Stars with M< 8 Msun lose their outer layers after the red giant phase and end up as white dwarfs. Which$of$these$ stars$will$have$ changed$the$ C B least$10$billion$ years$from$now?$ D A A © 2015 Pearson Education, Inc. Open+cluster:+A$few$thousand$loosely$packed$ stars$in$disk$of$our$galaxy$ Globular+cluster:++ P Up$to$106$stars$bound$by$gravity$into$a$dense$ball$$ P Found$in$the$halo$of$our$galaxy$ Stars$in$a$ cluster$are$ all$born$at$ same$@me.$ The$mainP sequence$ turnoff$point$ of$a$cluster$ tells$us$its$ age.$ Turnoff$point$of$ the$oldest$ globular$clusters$ below$Lsun;$ $ Implies$they$are$ >$1010$yrs$old!$ $ Oldest$are$$ ~13$Byr$old!$ $ Main$sequence$life@me$ t M / M M / M ms = sun ≈ sun t L / L 3 sun sun (M / M sun ) 2 ⎛ M sun ⎞ t ≈ 10 Byr ms ⎝⎜ M ⎠⎟ How do stars form? Star-Forming Clouds • Stars form in dark clouds of dusty gas in interstellar space.