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The Solar System. Our Star, the Sun. What is the Sun?. … a large ball of hydrogen gas that generates energy via nuclear fusion. Why?. It’s yellow (6000 K) … too hot for a liquid or solid. It’s made of more than 90% hydrogen …from spectroscopy.
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The Solar System Our Star, the Sun
What is the Sun? … a large ball of hydrogen gas that generates energy via nuclear fusion. Why? • It’s yellow (6000 K) … too hot for a liquid or solid • It’s made of more than 90% hydrogen …from spectroscopy • Its age (4.6 billion years) and luminosity (4 x 1023 KW)… too old for any ‘process’ other than fusion to generate that rate of energy output for that long
Lʘ = F • A A = 4 π R2 Lʘ = 4 x 1023 KW
Lord Kelvin (1824 – 1907) “I believe the tendency in the material world is for motion to become diffused, and that as a whole the reverse of concentration is gradually going on — I believe that no physical action can ever restore the heat emitted from the Sun, and that this source is not inexhaustible …”
Kelvin-Helmholtz Contraction The Sunformed a collapsing cloud of dust and gas The total gravitational potential energy lost in the collapse is … M⨀ and R⨀ are the mass and radius of the Sun, respectively. Assume that all of this energy is converted into heat. The Sun slowly radiates some of this heat as it slowly contracts. The rate at which the Sun gives off energy is its luminosity It radiates all its energy EGduring its lifetime τ… soτis
What Powers the Sun? Some Incredibly Efficient Process… the Conversion of Mass Into Energy!
Fusion: light nuclei bind together to form heavy Fission: heavy nuclei break apart to form light The energy releasedper fusion/fission event is called the binding energy. 1038 reactions convert 5 millions tons of mass into energy every second to keep the sun from collapsing! Still, only 0.7% of its mass will be lost this way.
The electromagnetic force repels nuclei of similar electric charge. If nuclei collide at high speeds and get close enough to touch, the strong force binds them together. This is nuclear fusion. It takes place in the core of stars where heavy nuclei are built out of lighter ones. Mass is lost in the process, which releases energy that powers the stars. Releases Energy.
Nuclear Fusion The bottom line 4 1H 4He + energy 1H = hydrogen (proton) 4He = helium-4 (alpha particle) Four hydrogen are fused into a single helium. Energy is released in the process. Einstein’s Famous Mass Energy Equivalence Principle E = mc2 Energy, E, equals mass, m, times the speed of light square, c2. The energy released in nuclear fusion comes from mass! Some mass is lost in each reaction and that amount of mass multiplied by the speed light squared is the energy released in that one reaction.
How Much Energy Is Generated Four hydrogen nuclei are converted into one helium nucleus… some mass “disappears” because 4 hydrogen nuclei “weigh” more than 1 helium nucleus. This mass loss Δm is converted into energy according to E =Δmc2 . Mass of hydrogen and heliumMass of four hydrogen 1 hydrogen = 1.673 x 10-27 kg 1 helium = 6.645 x 10-27 kg 4 hydrogen = 6.693 10-27 kg The energy, E, generated is… E = Δm c2 Δm = 4 hydrogen – 1 helium = (6.693 - 6.645) x 10-27 kg = 4.8 x 10-29 kg c = 300,000 km/s E = Δm c2 = 4.8 x 10-29 kg x (3 x 108 m/s)2 = 4.3 x 10-12 J 4.2 million tons of matter disappear every second to keep the Sun “burning” with a luminosity of 3.8 x 1023 kW!
How the Stars Work “I did not, contrary to legend, figure out the carbon cycle on the train home from Washington. I did, however, start thinking about energy production in massive stars upon my return to Ithaca. Because the observed energy production increased faster than the proton-proton reaction could explain, there had to be another reaction, and it had to involve heavier nuclei. Lithium, beryllium, and boron are the lightest elements heavier than helium. They could all be ruled out because of comparative scarcity. The next element is carbon. Repeated reactions of carbon with protons yielded a favorable result …the discovery of the CNO cycle took me about two weeks.” Hans Bethe (1906 – 2005)
Question The energy-generating mechanism that powers the Sun is _______. Kelvin-Helmholtz contraction, or release of gravitational energy as the Sun slowly contracts. windmills on the Sun driven by the Solar wind. ignition and burning of enormous amounts of carbon in the core. thermonuclear fusion of hydrogen into helium in the core. flexing of the Sun caused by Jupiter’s tidal forces.
The Sun’s Lifetime as a Normal Star How long will the Sun generate energy by fusing hydrogen into helium? The total available energy stored in the Sun in the form of mass, most of which is hydrogen, (according to Prof. Einstein) is— E⨀ = M⨀c2= 1.99 x 1030 kg x (3 x 108 m/s) 2 = 1.8 x 1047 J The Sun will fuse only 10% of its available hydrogen into helium. This fraction is f =0.10. The fusion process is only 0.7 % efficient, i.e., only 0.7% of the mass of the hydrogen is converted into energy when hydrogen is fused into helium. This conversion efficiency is ε =0.007. The total amount of energy released, ΔE, by nuclear fusion is— ΔE = ε f M⨀c2= 0.007 x 0.10 x E⨀ = 0.007 x 0.1 x 1.8 x 1047 J = 1.25 x 1044 J. The Sun’s luminosity is L⨀ = 3.9 x 1026 J/s. It’s estimated lifetime is—
Gravity and pressure in a stable star are in balance core Gravity tends to crush the star, which causes the temperature, pressure and density to increase toward the center. Density in the core is ~150 times that of water and the temperature is 15 million degrees Kelvin
This balance is called Hydrostatic Equilibrium At any ‘depth’ inside the Sun, the outward pressure caused by the hot, rapidly moving particles must support the weight of all the material above the layer. More weight must be supported at greater depth, so pressure must increase.
Downward pressure caused by weight of material above slab Upward pressure supports weight of slab plus weight of all material above the slab – hydrostatic equilibrium
Question The Sun has existed for 4.6 Gyr without much change in its size or appearance. Thus, it must be in hydrostatic equilibrium. To maintain this equilibrium, which two parameters must be in exact balance at every level within the Sun? Numbers of hydrogen and helium nuclei. Hydrogen gas pressure and helium gas pressure. Inward force of gravity and outward gas pressure. Magnetic field and force of gravity. Rate of sunspot appearance and disappearance.
A photon created in the core takes 1 million years to surface. A neutrino takes 2 seconds … why?
What About Those Pesky Neutrinos…? Neutrinos are produced by the weak nuclear force, which are among the nuclear reactions that take place in the core of the Sun. Most neutrinos escape from the Sun without interacting. Potentially, they could provide a direct view of the Sun’s core…if they could be detected! About 1,000,000,000,000 neutrinos pass through your body every second . On the average one of them will interact every 70 years! They can pass through a light year of lead.
Neutrino Production in Proton-Proton Chain Only electron neutrinos are produced
Problem – cosmic rays from outer space interact in atmosphere produce many particles which strike Earth and create havoc with a neutrino detector…if it’s on the Earth’s surface.
Homestake Mine Solar Neutrino Detector The Solar Neutrino Problem! Detect only 2.5 SNU’s … about 1/3 of what expected! 100,000 gallon tank of C2 Cl4 contains … 2 x 1030 atoms of Cl37! When neutrinos interact with chlorine, they produce a radioactive isotope of argon Expect about 7.5 SNU’s (40 radioactive Ar37 isotopes/month)
Many new generation detectors with greater capabilities have been built to solve the Solar Neutrino Problem
Elementary Particle Family 1 2 3 Neutrinos come in 3 flavors… …that can change into one another!
Another way to check the solar model…the “GONG” project …Helioseismometry… measure how the Sun vibrates
Question Which technique was used between the 1970’s and the 1990’s to measure solar neutrinos and led to a result known as the solar neutrino paradox? Measuring the rate of mutations in field mice, which readily absorb neutrinos. Measuring the interaction of neutrinos with the ozone layer. Measuring the proton-proton reaction in liquid hydrogen, where neutrinos act as intermediaries. Measuring how many times large church bells would ‘gong’ when struck by a neutrino. Production of radioactive argon nuclei by neutrino interaction with chlorine nuclei in a deep underground tank.
Light from limb originates higher in photosphere where it’s cooler and therefore darker