Nuclear Fusion Where Does the Sun Get Its Energy? Several light - PDF document

Nuclear Fusion Where Does the Sun Get Its Energy? • Several light nuclei (H) collide and combine to form a heavier • Life time is related to source of energy nucleus (He) – life time = (energy available) / (luminosity) • Gravitational Contraction? • Energy is released – Contraction due to gravity releases energy • Need high temperature and • Total energy due to contraction 10 48 ergs from Newton’s densities Laws – Must overcome electrostatic – life time = (10 48 ergs)/(4x10 33 erg/sec) = 10 7 years repulsion of like charged atomic • Radioactive decay, similar to heating of Earth? nuclei – Mostly H and He which do not decay, need heavy nuclei – Core of Sun is 15,000,000 K – Even if solid uranium it would produce 1/2 of energy seen – Density is 150,000 kg/m 3 Nuclear Physics Where Does the Energy Come From? • Elements specified by • Mass is converted directly into – Atomic number: Z = # of protons energy E=mc 2 – Protons have positive charge = +e – Einstein’s Famous relationship – Neutral atoms: #protons = #electrons – Mass and energy are the same thing! • Isotope specified by # of neutrons, N – The speed of light is very big so you get a lot of energy from a little bit of matter – Neutrons electrically neutral • 4 H → 1 He – All isotopes of a given element have same Z – Mass of H = 1.67252x10 -24 gm • Mass number: A=Z+N – Mass of He = 6.64258x10 -24 gm – A gives the number of nucleons – 4xH - He = 0.04750x10 -24 gm – Good indicator of mass – E = mc 2 = 4.75x10 -26 gm (3x10 10 cm/sec) 2 = 4.5x10 -5 ergs Structure of Matter Mass Number • Baryons: heavy particles – Neutrons, Protons • m p = 1.672623 X 10 -24 g • Finite size • Made of quarks • m n = 1.674929 X 10 -24 g • Leptons: light particles • m e = 9.109390 X 10 -28 g – Electrons, Neutrinos – Low rest mass m p ~ m n m p , m n >> m e – Unresolved in size – Not made up of quarks A = mass number • Quarks & Leptons fundamental particles 1

Fundamental Forces Strong Force • Forces are exchanged by virtual • Binds together n & p particles bosons • Short range ~10 -13 cm – Gravity - long range - gravitons • Mediated by mesons – Electromagnetic - long range - photons – Quark - anti-quark pair – Strong - short range - mesons Π meson - up/down quark, anti-quark pair – Weak - short range - weakons Weak Force Binding Energy • Amount of Energy needed to break • Protons & Neutrons interact via force nucleus apart into constituent p & n – Important for nuclear reactions in stars • Mediated by weakons or intermediate vector bosons • Range ~ 10 -15 cm • Converts proton into neutron & vice versa 1 0 n 1 1 p + 0 -1 e + 0 0 ν Beta Decay Conserves charge, baryons, leptons Energy From Fusion Coulomb Barrier • Converting Mass directly into energy is the most efficient way to get energy from matter • If 10% of solar Hydrogen is converted into He the Sun will shine at its current rate for 10 Billion Years 2

Proton-Proton CNO CYCLE Chain 1 2 3 4 5 6 Triple Alpha Reactions Fusion of Heavier Elements Helium burning begins when Temp > 10 8 K • To fuse heavier elements you need hotter temperatures to overcome Coulomb barriers 2 Z 2 2 e 4 µ /3kh 2 T ~ 4 Z 1 • Alpha Reactions 8 Be is unstable and decays into 2 He nuclei (alpha particles in 2.6x10 -16 sec • Carbon, Oxygen, Silicon fusion To produce C requires the almost simultaneous collision of 3 alpha particles Need high cross section Alpha Reactions Carbon Burning • During He burning some of C produced reacts with He to form O which in turn reacts When He in core is gone to form Ne, then Mg….. Temperature ~ 5-8 x 10 8 K • Reactions rare and not major source of energy generation • Examples: 12 C + 4 He 16 O + γ 16 O + 4 He 20 Ne + γ 20 Ne + 4 He 24 Mg + γ 3

Silicon Burning Oxygen Burning 28 Si + 28 SI 56 Ni + γ 56 Ni 56 Fe + 2e + +2 ν e T ~ 10 9 K At T > 10 9 K, photon energies are large enough to destroy certain nuclei Photonuclear reactions or photodissociations Formation of Heavier Elements Formation of elements heavier than Fe require an input of energy and cannot be produced by thermonuclear reactions Produced almost exclusively by neutron capture during final violent stages of stellar evolution (e.g. supernovae) K. Langanke Solar Neutrinos Solar Neutrinos • Neutrinos • 3 different neutrino – Very low mass particles produced as a experiments are sensitive side product of nuclear fusion to neutrinos from different – They hardly interact with matter so they nuclear reactions can travel completely out of the Sun undisturbed • The measured points do • Detection of Neutrinos not agree very well with the – Difficult since they interact so weakly with matter predicted number of each – Takes very large detectors type of neutrino – Several have been built to detect different • There is a problem with the types of neutrinos from inside the sun Standard Model 4

The Main Sequence Revisited The Main Sequence Revisited • All stars arrange themselves • All Stars are made up of to balance the force of gravity mostly H and their interior pressure • Core burning of H will – As mass increases gravity increases continue for long time • Differential Pressure increases • Structure will change slowly inside stars • Energy generation + luminosity – HYDROSTATIC increases EQUILIBRIUM • Temperature + size increase to let increased energy out • This equilibrium sequence of mass is the Main Sequence The Main Sequence Revisited Question • Mass Limits – M < 0.08 M solar • Remember that the luminosity of a star • No Fusion was found be to closely related to its mass (L ∝ M 4 ). Now we know that stars – M > 90 M solar get their energy by converting their • Radiation Pressure mass directly into energy so the total dominates Gravity amount of energy a star has is proportional to its mass (E ∝ M). Will a massive star live a longer or shorter time than a low mass star? The Main Sequence Revisited Question • Like the Sun all stars arrange themselves to balance the force of • Remember that the luminosity of a star gravity and their interior pressure was found be to closely related to its – As mass increases gravity increases mass (L ∝ M 4 ). Now we know that stars • Pressure increases inside stars get their energy by converting their • Energy generation + luminosity increases mass directly into energy so the total • Temperature + size increase to let amount of energy a star has is increased energy out proportional to its mass (E ∝ M). Will a • This equilibrium sequence of mass massive star live a longer or shorter is the Main Sequence time than a low mass star? 5

Solar Neutrinos Solar Neutrinos • Neutrinos • 3 different neutrino – Very low mass particles produced as a experiments are sensitive side product of nuclear fusion to neutrinos from different – They hardly interact with matter so nuclear reactions they can travel completely out of the Sun undisturbed • The measured points do • Detection of Neutrinos not agree very well with the – Difficult since they interact so weakly predicted number of each with matter type of neutrino – Takes very large detectors • There is a problem with the – Several have been built to detect different types of neutrinos from inside Standard Model the sun Energy Energy Transport Transport • Massive Stars M > 1.2 M solar – Core: • CNO cycle • Convective core • Steep thermal gradient • Energy generation rate changes quickly • Radiation no efficient enough to transport out all energy being released – Outside Core: • Radiation carries energy Energy Energy Transport Transport • Low Mass Stars • Low Mass Stars M < 1.2 M solar – Core: As mass decreases, H- zone moves deeper into star due to lower Temperatures • PP Chain • Small thermal gradient M < 0.3 M solar Fully convective • Radiative transport efficient – Near Surface: • H- opacity becomes large - Temp low enough for H to be partially ionized • Increase in opacity makes convection more efficient • Convection zones 6