Results of Exam 2

1. Results of Exam 2 Congratulations!! Lecture 17

2. What Makes the Sun Shine? • The Sun puts out 4 x 1026 watts • That’s a very large amount • The typical power plant puts out 1000 megawatts • 109 watts • 10,000 power plants put out 1013 watts • The Sun has been shining for about 4.5 billion years • What is a watt? • A watt is a unit of power • Energy per unit time • Joule/sec Lecture 17

3. Thermal and Gravitational Energy • If the Sun were made of coal and its energy came from burning, it could only burn at its present rate for a few thousand years • Conservation of energy states that energy cannot be created or destroyed, only converted from one kind to another • 19th century scientists speculated that the Sun’s energy resulted from meteorites falling into the Sun • Calculations showed that in 100 years, the mass of meteors would equal the mass of the Earth and that the period of the Earth’s orbit would be changed by 2 seconds a year Lecture 17

4. Gravitational Contraction • Around 1850, Helmholtz and Kelvin proposed that the Sun might produce energy by converting gravitational energy to heat • A shrinking of 40 m per years would be sufficient • Would keep Sun shining for 100 million years • In the 19th century, that seemed long enough • In the 21st century, we know that the Sun and the Earth are much older than 100 million years • A new source of energy had to be understood in the 20th century Lecture 17

5. Mass, Energy, and Relativity • Einstein formulated the idea that mass and energy are interchangeable • Mass can be converted to energy • Energy can be converted to mass • E = mc2 • Special case of E2 = (mc2)2 + (pc)2 • p is the momentum of the mass • At rest, p=0, and we get E = mc2 • Energy is equal to mass times a constant • c is the speed of light, 3 x 108 meters/second • c2 is a very large number • Converting even a small amount of mass creates a lot of energy Lecture 17

6. Mass to Energy • The vast power of nuclear reactors and weapons results from the fact that relatively large amounts of mass are changed to energy in nuclear reactions • Often one hears that E=mc2 applies only to nuclear reactions and nuclear explosions • However, ordinary chemical burning (wood, gasoline, etc.) also involves a change of mass to energy • Very small change in mass • A million times smaller than in nuclear processes • We know that mass can be converted to energy • But how?? Lecture 17

7. Elementary Particles • The fundamental components of matter are called elementary particles • The physical objects around us are made of molecules and atoms, matter • Molecules are groups of atoms • Atoms are made of neutrons, protons, and electrons • The electron is an elementary particle • Protons and neutrons in turn are made of elementary particles called quarks and gluons • Antimatter is composed of antiprotons, antineutrons, and antielectrons (positrons) • When matter comes into contact with antimatter, they annihilate each other Lecture 17

8. The Standard Model • Within the Standard Model, we think that there are 6 kinds of quarks, 6 kinds of leptons, and 4 types of exchange particles • Nothing else! • Quarks • Up, down, strange, charm, bottom, top • Leptons • Electron, muon, tau, electron neutrino, muon neutrino, tau neutrino • Exchange particles • Represent the four fundamental forces • Photon, gluon, W and Z bosons, graviton (not observed) Lecture 17

9. The Atomic Nucleus • Most of the mass of an atom is concentrated in the nucleus • The nucleus is made of neutrons and protons bound together by the attractive strong force • The strong force easily overwhelms the electromagnetic force of the protons trying to repel each other in the nucleus • When neutrons and protons are brought together, they are held together by the strong force and binding energy is released • The mass of the bound system is less than the mass of the constituent neutrons and protons • E = mc2 Lecture 17

10. Fusion and Fission • The most well bound nucleus is 56Fe (iron 56) • 26 protons and 30 neutrons • Lighter nuclei and heavier nuclei are less well bound • Thus we can bind together lighter nuclei to produce more well bound nuclei and release energy (fusion) • Alternatively, we can break up heavier nuclei (like uranium) into lighter nuclei and release energy (fission) Lecture 17

11. The Fuel Cycle of the Sun • The main fuel cycle of the Sun involves burning hydrogen to helium • Fusing 1 kg of hydrogen to helium using this process produces 6.4 x 1014 J which is more than 10 times the Earths annual consumption of electricity and fossil fuels • The Sun converts 600 million tons of hydrogen to helium every second Lecture 17

12. The Interior of the Sun • Fusion in the center of the Sun can only occur if the temperature is very high • Our knowledge of the center of the Sun relies on computer models • The Sun must change • The Sun is burning hydrogen to helium • Will the Sun get brighter or fainter? • Will the Sun get larger or smaller? • Ultimately the Sun will burn up all its fuel • We will use all of our observations of the Sun to constrain the model and calculate things we cannot observe directly Lecture 17

13. Observations of the Sun • The Sun is a gas • High temperatures mean high pressures • The Sun is stable • All the forces in the Sun are balanced • Gravitational forces trying to collapse the Sun are balanced by the outward pressure of the hot gasses • Hydrostatic equilibrum • The Sun is not cooling down • The Sun radiates energy but generates enough to maintain its temperature Lecture 17

14. Heat Transfer in a Star • Heat is transferred three ways in a star • Conduction • Atoms collide with nearby atoms • Convection • Currents of warm material rise • Radiation • Energetic photons move away and are absorbed elsewhere • The gasses of the Sun are opaque to radiation • Opacity • It takes 1 million years for a photon generated deep in the Sun to reach the surface • Neutrinos escape in about 2 seconds Lecture 17

15. Model Stars • To describe the parts of the Sun we cannot observed directly, a model star is created • Energy is generated through fusion in the core of the star which extends 1/4 of the way to the surface • The core contains 1/3 of the mass of the star • Temperatures reach 15 million K and the density is 150 times the density of water • The energy is transported toward the surface by radiation until it reaches 70% of the distance from the center to the surface where convection takes over Lecture 17

16. Solar Pulsations • Astronomers have observed that the Sun pulsates • Pulsations are measured by measured the radial velocity of the surface • The pulsation cycle is typically about 5 minutes • These pulsation can be related to solar models • Solar seismology • Measurements using solar seismology have sown that convection occurs 30 % of the way to the center • Differential rotation persists down through the convection zone • Helium concentration in the interior of the Sun is similar to the surface Lecture 17

17. Solar Neutrinos • Neutrinos are created in the solar fusion process • Neutrinos escape without much interference • About 3% of the Sun’s generated energy is carried away by neutrinos • 3.5 x 1016 solar neutrinos pass through each square meter of the Earth every second • First experiments to measure solar neutrinos found only 1/3 as many as predicted • Recent experiments have found about 1/2 as many as predicted Lecture 17

18. Neutrino Oscillations • One explanation for the solar neutrino problem is that neutrinos oscillate back and forth between the various kinds of neutrinos • The sun produces only electron neutrinos • En route to the Earth, the electron neutrinos may spontaneously turn into muon neutrinos that are not detected • Another problem is the knowledge of the neutrino mass • Standard model says the neutrino has no mass • If the neutrino has mass, then many possibilities are open • As we speak, experimenters are trying to measure the mass of the neutrino • Science marches on Lecture 17

19. Analyzing Starlight • Stars are not all the same • Some are bright and some are dim • They have different colors • Color is a good indication of the temperature of the star • Red is the coolest • Blue is the warmest Stars in the constellation Orion Lecture 17

20. The Brightness of Star • Luminosity • The total amount of energy emitted per second • Stars give off energy in all directions • Very little actually reaches our eyes or telescopes • The amount of light we see is called the apparent brightness • If stars all had the same luminosity, then we could tell how far away they were by their apparent brightness • Wrong! Lecture 17

21. The Magnitude Scale • Historically, the brightness of a star was classified using magnitudes • The larger the magnitude, the fainter the star • Originally, magnitudes of stars were assigned by eye • In the 19th century, the system of magnitudes was quantified and the definition that magnitude 1 stars (the brightest) were 100 times brighter than magnitude 6 stars (the dimmest) • Each magnitude is brighter by a factor of 2.512 Lecture 17

22. Colors of Stars • To find the exact color of a star, astronomers filter the light through three filters • U (ultraviolet), 360 nanometers • B (blue), 420 nanometers • V (visual, for yellow), 540 nanometers • The difference between the magnitude measured through any two of the filters is called the color index • For example, B - V • The total magnitude of the star does not affect its color but its temperature does • By agreement, B - V = 0 corresponds a temperature of 10,000 K • B - V = -0.4 corresponds to a hot blue star • B - V = +2 corresponds to a cool red star • The Sun has B - V = 0.62 corresponding to a temperature of 6000 K Lecture 17

23. The Spectra of Stars • Astronomers can analyze the wavelength of the light emitted by stars and determine what elements are present in the stars • However, the main reason that stellar spectra look different for different stars is the temperature of the stars • Hydrogen is the most abundant element and, depending on the temperature of the star, can be difficult to see spectroscopically • Very cool stars have absorption lines in the UV • Very hot stars have their hydrogen completely ionized and there can be no absorption lines from hydrogen • Around 10,000 K is optimum for observing hydrogen Lecture 17

24. Classification of Stellar Spectra • Stars are classified by their temperatures into seven main spectral classes • O, B, A, F, G, K, M • O is the hottest, M is the coolest • Each class is further subdivided into ten subclasses • A0, A1, A2,…, with A0 being the hottest • The system came from looking at the spectra of stars and classifying them according to how complicated they were Lecture 17

25. Abundances of the Elements • By analyzing the spectra of stars, one can identify elements in the star • Laboratory measurements are done for the elements at different temperatures • Many factors make the identification difficult • Temperature and pressure may make certain elements invisible • Motion of the star’s surface and rotation of the star can blue the absorption lines • Measurements show that hydrogen makes up 75% of the mass of most stars and helium makes up 25% with a few percent left for the other elements Lecture 17

26. A Stellar Census • The lifetime of stars is long compared with human existence • Studying one star can give some information but not everything we want to know about stars • We need to study a large number of stars to learn their secrets • Stars are very far away so we use the unit light year (LY) to measure distances to stars • The distance light travels in 1 year • 9.5 x 1012 km Lecture 17

27. Luminosities of Nearby Stars • Let’s look at the stars in our “immediate” neighborhood • Within 12 LY of our Sun • We can immediately see that the Sun is one of the brightest stars in our neighborhood • Only 3 magnitude=1 stars are in this group • Most magnitude=1 stars are far away • Most are hundreds of LY away Lecture 17

28. Top 30 Brightest Stars • Shown on the left are the 30 brightest stars as seen from Earth • The most luminous is 100,000 time more luminous than the Sun • There are no stars that bright near to us • Stars with low luminosity (0.01Lsun to 0.0001Lsun) are very common • A star with L=0.01Lsun cannot be seen unless it is closer than 5 LY Lecture 17

29. Density of Stars in Space • What is the typical spacing between stars? • There are 59 stars with 16 LY of Earth • Stars are very far apart • Stars are very dense objects with lots of space between them Lecture 17

30. Stellar Masses • We know that the Sun is relatively luminous • How does the mass of the Sun compare with other stars? • A nice way to measure the masses of stars is by studying binary star systems • Roughly half of stars exist as binaries • The first binary star was discovered in 1650 • Mizar in the middle of the Big Dipper’s handle • The star Castor in the constellation Gemini is also a binary Lecture 17

31. Observing Binary Stars • Visual binaries • Both star cans be seen using an optical telescope • Sometimes the two stars are not actually close to each other but only appear to be close • Spectroscopic binaries • Spectroscopic lines change with regular period • Only one star is visible • Recent measurements showed that Mizar was actually two sets of binary stars Lecture 17

32. Masses from the Orbits of Binary Stars • We can estimate the masses of binary star systems using • D3 = (M1+M2)P2 • M1+M2 is the mass of the binary system in units of the Sun’s mass Lecture 17

33. Range of Stellar Masses • How large can the mass of a star be? • Most stars are smaller than the Sun • There are a few stars known with 100 Msun • The smallest stars have masses of about 1/12 Msun • Objects with masses of 1/100 to 1/12 Msun may produce energy for a short time • Brown dwarfs • Similar in size to Jupiter but 10 to 80 times more massive • Failed stars • Difficult to observe • Hydrogen cannot fuse to helium R 136, a cluster with stars as masive as 100 MSun Lecture 17

34. Lithium Thermometer • How can we tell a brown dwarf from a small, cool star • Lithium (3 protons and 4 neutrons) cannot exist in an active star • Convection will take the lithium down into the hot parts of the star and destroy it Brown dwarf Gliese 229B Lecture 17

35. Mass Luminosity Relation • Are the mass and luminosity of stars related? • Yes • The more massive the star the more luminous • About 90% of all stars obey the relationship shown to the right Lecture 17

36. Diameters of Stars • The diameter of the Sun is easy to measure • Measure the angle (0.5), measure the distance, get the diameter (1.39 million km) • All other stars appear to be a point in a telescope • The diameter of some stars have been measured by studying the dimming of the star’s light as the Moon passes in front of it • The diameter of some stars have been measured using eclipsing binaries Lecture 17