# Why do stars shine? emit thermal (~blackbody) radia=on heat leaks out of their photospheres. Luminosity = rate of energy loss.

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1 Astronomy 101

2 Why do stars shine? Stars shine because they are hot. emit thermal (~blackbody) radia=on heat leaks out of their photospheres. Luminosity = rate of energy loss. To stay hot, stars must make up for the lost energy, otherwise they would go out.

3 Case Study: The Sun Ques=on: How long can the Sun shine? Answer: Consider the internal heat content of the Sun. Luminosity = rate of heat loss. Life=me = Internal Heat Luminosity

4 What if no source of energy? The Sun s Luminosity losses would not be balanced by input of new internal heat. The Sun would steadily cool off & fade out. 18th Century: Assumed a solid Sun (iron & rock) Found Life=me ~ 10 Million Years No Problem: Earth was thought to be thousands of years old.

5 The Age Crisis: Part I Late 1800s: Geologists: Earth was millions of years old. How can Earth be older than the Sun? Astronomers: The Sun is a big ball of gas in Hydrosta/c Equilibrium. Kelvin & Helmholtz proposed Gravita/onal Contrac/on as a source of energy.

6 Kelvin Helmholtz Mechanism Luminosity radiates away heat Outer layers of the Sun cool at li]le, lowering the gas pressure. Lower Pressure means Gravity gets the upper hand and the star contracts a li]le. Contrac=on compresses the core, hea=ng it up a li]le, adding heat to the Sun. Sun could shine for ~100 Million years

7 Gravity & Pressure in Equilibrium G P

8 Luminosity radiates away heat & Pressure Drops G P

9 Balance tips in favor of gravity, Sun shrinks. G P

10 Contraction makes core heat up, increasing the internal Pressure. G P

11 Balance restored, but with higher gravity, pressure & temperature than before... G P Starts the cycle all over again...

12 The Age Crisis: Part II Early 1900s: Geologists show that the Earth is >2 Billion years old. Kelvin Says: The Geologists are wrong. Nature Says: Kelvin is wrong... There is new physics.

13 Nuclear Fusion 1905: Einstein demonstrates that Mass and Energy are equivalent: E=mc s: Eddington noted that 4 protons have 0.7% more mass than 1 Helium nucleus (2p+2n). If 4 protons fuse into 1 Helium nucleus, the remaining 0.7% of mass is converted to energy.

14 Fusion Energy Fuse 1 gram of Hydrogen into grams of Helium. Lehover grams converted into Energy: E = mc 2 = 6.3x10 18 ergs Enough energy to lih 64,000 Tons of rock to a height of 1 km.

15 Hydrogen Fusion Ques=on: How do you fuse 4 1 H (p) into 4 He (2p+2n)? Issues: Four protons colliding at once is unlikely. Must turn 2 of the protons into neutrons. Must be hot: >10 Million K to get protons close enough to fuse together.

16 Proton Proton Chain: 3-step Fusion Chain

17 neutrino 2 H positron photon 3 He 4 He 3 He 2 H positron photon neutrino

18 The Bo]om Line Fuse 4 protons ( 1 H) into one 4 He nucleus. Release energy in the form of: 2 Gamma ray photons 2 neutrinos that leave the Sun 2 positrons that hit nearby electrons, crea=ng two more Gamma ray photons Mo=ons (heat) of final 4 He and 2 protons.

19 The Age Crisis: Averted Luminosity of the Sun is ~4x10 33 erg/sec Must fuse ~600 Million Tons of H into He every second. ~4 Million tons converted to energy per second. Sun contains ~10 21 Million Tons of Hydrogen Only ~10% is hot enough for fusion to occur. Fusion Life=me is ~10 Billion Years.

20 Test: Solar Neutrinos Ques=on: How do we know that fusion is occurring in the core of the Sun? Answer: Look for the neutrinos created in Step 1 of the Proton Proton chain.

21 What are Neutrinos? Massless, weakly interac=ng neutral par=cles. Travel at the speed of light. Can pass through a block of lead 1 parsec thick! Any neutrinos created by nuclear fusion in the Sun s core would stream out of the Sun at the speed of light.

22 Solar Neutrinos: Observed! Detec=on of neutrinos is very hard: Need massive amounts of detector materials Work underground to shield out other radia=on Answer: We detect neutrinos from the P P chain in all the experiments performed to date! Success! But...

23 The Solar Neutrino Problem We detect only ~1/3 of the number expected... Why? Is our solar structure model wrong? Is the subatomic par=cle theory of neutrinos wrong? The last seems most plausible recent evidence neutrinos have mass ques=on for the physics of 21st century!

24 Purng Stars Together Physics needed to describe how stars work: Law of Gravity Equa=on of State ( gas law ) Principle of Hydrosta=c Equilibrium Source of Energy (e.g., Nuclear Fusion) Movement of Energy through star

25 Hydrosta=c Equilibrium Balance between Pressure & Gravity. If Pressure dominates, the star expands. If Gravity dominates, the star contracts. Sets up a Core Envelope Structure: Hot, dense, compact core. Cooler, low density, extended envelope.

26 Hydrosta=c Equilibrium Gravity Gas Pressure

27 Energy Genera=on Stars shine because they are hot. To stay hot stars must make up for the energy lost by shining. Two Energy sources available: Gravita=onal Contrac=on (Kelvin Helmholtz) Only available if star is NOT in equilibrium Nuclear Fusion in the hot core.

28 Main Sequence Stars Generate energy by fusion of 4 1 H into 1 4 He. Proton Proton Chain: Relies on proton proton reac=ons Efficient at low core Temperature (T C <18M K) CNO Cycle: Carbon acts as a catalyst Efficient at high core Temperature (T C >18M K)

29 Proton Proton Chain:

30 CNO Cycle:

31 Controlled Nuclear Fusion Fusion reac=ons are Temperature sensi/ve: Higher Core Temperature = More Fusion ε(pp) ~ T 4 ε(cno) ~ T 18 BUT, More fusion makes the core hober, HoBer core leads to even more fusion, Why doesn t it blow up like an H Bomb?

32 Hydrosta=c Thermostat If fusion reac=ons run too fast: core heats up, leading to higher pressure pressure increase makes the core expand. expansion cools core, slowing fusion. If fusion reac=ons run too slow: core cools down, leading to lower pressure pressure drop makes the core contract. contrac=on heats core, increasing fusion.

33 Thermal Equilibrium Heat always flows from ho]er regions into cooler regions. In a star, heat must flow: from the hot core, out through the cooler envelope, to the surface where it is radiated away as light.

34 Energy Transport There are 3 ways to transport energy: 1) Radia=on: Energy is carried by photons 2) Convec=on: Energy carried by bulk mo=ons of gas 3) Conduc=on: Energy carried by par=cle mo=ons

35 Radia=on Energy is carried by photons. Photons leave the core Hit an atom or electron within ~1cm and get sca]ered. Slowly stagger to the surface ( random walk ) Break into many low energy photons. Takes ~1 Million years to reach the surface.

36 Random Walk

37 Convec=on Energy carried by bulk mo=ons of the gas. Analogy is water boiling: Hot blob rises cooler water sinks

38 Conduc=on Heat is passed from atom to atom in a dense material from hot to cool regions. Analogy: Holding a spoon in a candle flame, the handle eventually gets hot.

39 Energy Transport in Stars Normal Stars: A mix of Radia=on & Convec=on transports energy from the core to the surface. Conduc=on is inefficient (density is too low). White Dwarfs: Ultra dense stars Conduc=on dominates energy transport.

40 Summary: Stars shine because they are hot. need an energy source to stay hot. Kelvin Helmholtz Mechanism Energy from slow Gravita/onal Contrac/on Cannot work to power the present day Sun Nuclear Fusion Energy Energy from Fusion of 4 1 H into 1 4 He Dominant process in the present day Sun

41 Summary: Energy genera=on in stars: Nuclear Fusion in the core. Controlled by a Hydrosta=c thermostat. Energy is transported to the surface by: Radia=on & Convec=on in normal stars Conduc=on in white dwarf stars With Hydrosta=c Equilibrium, these determine the detailed structure of a star.

42 Ques=ons Do other stars also produce energy by nuclear fusion? Why doesn t the Sun explode? How long can other stars last? Are there other objects that shine via gravita=onal contrac=on?

43 Ques=ons Which stars generate energy primarily via the CNO cycle and which by the PP cycle? Why are MV stars less luminous than GV stars? OV more luminous? What will happen when a star runs out of fuel? What is going on in Supergiants? Giants?

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