Chapter 11: Our Star

Lecture Outline

—Einstein, 1905

It is powered by NUCLEAR ENERGY! Nuclear Potential Energy (core) ~ 10 billion years Luminosity

Contraction stopped when fusion started replacing the energy radiated into space.

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?

Big nucleus splits into Small nuclei stick together smaller pieces. to make a bigger one.

(Nuclear power plants) (Sun, stars)

OUT 4He nucleus 2 gamma rays 2 positrons 2 neutrinos

Total mass is 0.7% lower.

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.

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.

• Because it is burning. • Because of its chemical energy. • Because of its gravitational energy. • Because of nuclear fusion. • Because of nuclear fission.

• 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.

• A temperature of millions of degrees • High density • The presence of uranium • All of the above • A and B

Observations of these solar neutrinos can tell us what's happening in the core.

More recent observations find the right number of neutrinos, but some have changed form.

Are cooler than other parts of the Sun's surface (4000 K).

Are regions with strong magnetic fields.

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(

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. • The gas between the stars is called the interstellar medium. Thought Question

What would happen to a contracting cloud fragment if it were not able to radiate away its thermal energy?

A. It would continue contracting, but its temperature would not change. B. Its mass would increase. C. Its internal pressure would increase. Cloud heats up as gravity causes it to contract due to conservation of energy. Contraction can continue if thermal energy is radiated away. As gravity forces a cloud to become smaller, it begins to spin faster and faster, due to conservation of angular momentum. As gravity forces a cloud to become smaller, it begins to spin faster and faster, due to conservation of angular momentum. Gas settles into a spinning disk because spin hampers collapse perpendicular to the spin axis. Formation of Jets

Rotation also causes jets of matter to shoot out along the rotation axis.

What would happen to a protostar that formed without any rotation at all?

A. Its jets would go in multiple directions. B. It would not have planets. C. It would be very bright in infrared light. D. It would not be round.

1. Gravity causes gas cloud to shrink and fragment. 2. Core of shrinking cloud heats up. 3. When core gets hot enough, fusion begins and stops the shrinking. 4. New star achieves long-lasting state of balance

• How do stars form? – Stars are born in cold, relatively dense molecular clouds. – As a cloud fragment collapses under gravity, it becomes a protostar surrounded by a spinning disk of gas. – The protostar may also fire jets of matter outward along its poles.

than 300MSun would blow apart. • Stars less massive

than 0.08MSun can't sustain fusion.

The main form of pressure in most stars Degeneracy Pressure:

Particles can't be in same state in same place

Doesn't depend on heat content

• How massive are newborn stars?

– Stars greater than about 300MSun would be so luminous that radiation pressure would blow them apart. – Degeneracy pressure stops the contraction of

objects <0.08MSun before fusion starts. H-R diagram of old, evolved globular cluster Thought Question

What happens when a star can no longer fuse hydrogen to helium in its core?

A. Its core cools off. B. Its core shrinks and heats up. C. Its core expands and heats up. D. Helium fusion immediately begins.

• As the core contracts, H begins fusing to He in a shell around the core. • Luminosity increases because the core thermostat is broken—the increasing fusion rate in the shell does not stop the core from contracting. Life Track of a Sun-Like Star Death of low-mass star: Planetary Nebula + White Dwarf

white dwarf Thought Question

What happens when a star's core runs out of helium?

A. The star explodes. B. Carbon fusion begins. C. The core cools off. D. Helium fuses in a shell around the core. End of Fusion

• Fusion progresses no further in a low-mass star because the core temperature never grows hot enough for fusion of heavier elements (some He fuses with C to make oxygen). • Degeneracy pressure supports the white dwarf against gravity. What have we learned?

• What are the life stages of a low-mass star? – H fusion in core (main sequence) – H fusion in shell around contracting core (red giant) – He fusion in core (horizontal branch) – Double shell–fusion (red giant) • How does a low-mass star die? – Ejection of H and He in a planetary nebula leaves behind an inert white dwarf.

• Late life stages of high-mass stars are similar to those of low-mass stars: – Hydrogen core fusion (main sequence) – Hydrogen shell fusion (supergiant) – Helium core fusion (supergiant)

Core temperatures in stars with >8MSun allow fusion of elements as heavy as iron. © 2015 Pearson Education, Inc. Advanced reactions in stars make elements such as Si, S, Ca, and Fe. © 2015 Pearson Education, Inc. Multiple Shell Burning

• Advanced nuclear burning proceeds in a series of nested shells.

change in kinetic change in gravitational = energy potential energy

(escape velocity)2 G × (mass) = 2 (radius) V 2 GM e = 2 R Radius of a black hole’s “event horizon”

• Radius at which escape speed equals speed of light 2 – Ve = 2GM/R 2 – If we set Ve = c, then Rbh= 2GM/c

• Plugging in G and c, get:

M Rbh = 3 km M sun Neutron star

3 MSun black hole

The event horizon of a 3MSun black hole is also about as big as a small city. A black hole's mass strongly warps space and time in the vicinity of the event horizon.

• Nothing can escape from within the event horizon because nothing can go faster than light.

• No escape means there is no more contact with something that falls in. It increases the hole's mass, changes its spin or charge, but otherwise loses its identity.

How does the radius of the event horizon change when you add mass to a black hole? A. It increases. B. It decreases. C. It stays the same.

3MSun black hole would be lethal to humans.

Tidal forces would be gentler near a supermassive black hole because its radius is much bigger. Do black holes really exist?

Some X-ray binaries contain compact objects of mass exceeding 3MSun that are likely to be black holes.

One famous X-ray binary with a likely black hole is in the constellation Cygnus. What have we learned?

• What is a black hole? – A black hole is a massive object whose radius is so small that the escape velocity exceeds the speed of light. • What would it be like to visit a black hole? – You can orbit a black hole like any other object of the same mass—black holes don't suck! – Near the event horizon, time slows down and tidal forces are very strong. What have we learned?

• Do black holes really exist? – Some X-ray binaries contain compact objects too massive to be neutron stars—they are almost certainly black holes.