LIVES AND DEATHS OF STARS
LIVES AND DEATHS OF STARS AST 309N
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This 17 page Class Notes was uploaded by Keegan Goyette on Sunday September 6, 2015. The Class Notes belongs to AST 309N at University of Texas at Austin taught by Staff in Fall. Since its upload, it has received 62 views. For similar materials see /class/181760/ast-309n-university-of-texas-at-austin in Astronomy at University of Texas at Austin.
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Date Created: 09/06/15
Ast 309N quotsmegmaquot 1 REVIEW OF BASIC CONCEPTS A Scientific Measurements Measurements require one to quantify physical properties 1 Scientific Notation 4T5 x 104 45000 decimal part power of ten exponent 4 Necessary to deal with very large and very small numbers eg atomic nucleus is 10 20 x earth s radius superclusters of galaxies are 1020 x earth s radius Combining numbers in scientific notation treat decimal part normally addsubtract exponents when multiplyingdividing Proportionality direct and inverse constant of proportionality DvtaDoctvconstant v voc t t T proportional sign Squares and cubes area of sphere 4139cr2 volume of sphere 21 2 Scientific Units Fundamental Units standard units 2 metric mass 1 gram 2 0022 lbs length l centimeter inch time 1 second energy 1 erg energy of a ying mosquito temperature 1 degree Kelvm 0 K absolute zero 1998 Harriet L Dinerstein Astronomy 309N Stars and Stellar Evolution 273 K 0 C 2 32 F 300 K 27 C 2 80 F Manipulating Numbers in Scientific Notation Procedure 1 Write out the operation in full scientific notation 2 Rearrange putting the numeral parts together separate from the powers of ten 3 Combine the numerical parts then combine the powers of ten Example 1 2 x 104 x 3 x 106 2 x 3 x 104 x106 6 X 104l6 6 X1010 Example 2 The Sun has a mass of2 gtlt 1033gm It is composed of individual particles mostly protons each of which has a mass of 1 atomic mass unit 16 x 103924gm How many protons are there in the sun 1M0 2 x 1033gm l amu 16 x 10 24gm 2 X 1033 gm No of protons 16 x 103924 gmproton gtlt 1033393924 protons 12 x 103324 protons 12 x 1057protons Notice that units are carried along and can be cancelled in numerator and denominator 1998 Harriet L Dinerstein Astronomy 309N Stars and Stellar Evolution Convenient Units depends on context Property Standard Unit Convenient Unit Application Distance 1 cm 1 Angstrom wavelengths of light 10398cm l Astronomical Unit distance from earth to sun 1AU15 gtlt 1013cm l parsec 31 x 1018cm distances between stars Mass 1 gm 1 solar mass masses of stars galaxies 2 x 1033 MO Velocity l cmsec l kmsec 103cmsec velocities of stars galaxies 2000 mihr Luminosity l ergsec l kiloWatt 101 ergsec 1 solar luminosity luminosities of stars 2 4 x 1033ergsec galaxies Angle radians degrees minutes and Moon Sun 2 30 arc min seconds of arc B ENERGY MOMENTUM FORCE Matter in Motion 1 Forms of Energy Kinetic energy 2 energy of motion mv2 Potential energy 2 energy stored in the relative positions of objects which feel a force can be either gravity or electric force Thermal or heat energy 2 energy of random internal motions of atoms or molecules in a gas liquid or solid Temperature measures the average random kinetic energy of the atoms and therefore their velocities Absolute zero corresponds to zero velocity Radiation or light 2 electromagnetic energy The governing rule is conservation of energy You cannot change the total amount of energy in a system you can only convert one kind into another Example re entry of the Space Shuttle into the atmosphere potentiala kinetica thermal heat tiles 1998 Harriet L Dinerstein Astronomy 309N Stars and Stellar Evolution Nuclear energy an exception No Einstein s theory of special relativity says that matter and energy are equivalent or that matter is just another form of energy Conversion factor is lar e39 E mc lgm 9 x 1020 erg Note Comparing kinetic with thermal energy Kinetic energy as defined here is macroscopic systematic motion such as a thrown eraser thermal energy is the microscopic random motion of the atoms within the eraser corresponding to the fact that the eraser feels warm 2 Momentum Conservation of Momentum is another major principle of physics You already know it at least intuitively Momentum 2 mass gtlt velocity Things don t move unless they re pushed or more exactly a body will continue in uniform motion or at rest until a force is exerted on it This also goes for zero velocity inertia g 100W light bulb for 30000 yrs Angular Momentum is the momentum associated with rotating objects Conservation of angular momentum 2 mass gtlt velocity gtlt radius keeps a body spinning at a constant rate earth pulsars It also predicts that if you take a large spinning object and make it smaller it will spin faster ice skater 3 Fundamental Forces field forces which act at a distance Force Relative Acts On Range Action Application Strength Gravity 6 x 10 59 all matter infinite attracts holds massive bodies in orbit Electro 10391 charged infinite attracts or holds atoms magnetic particles repels molecules solids together Weak 10 4 subatomic lt 10 14 cm converts nuclear particles once kind of reactions particle into radioactive another decay Strong 1 subatomic lO39U binds atomic particles 10 14cm nuclei together Unifying theories describe different forces as simply different aspects of a single force electroweak Weinberg Salaam GUT s bring together electric weak and strong forces 1998 Harriet L Dinerstein Astronomy 309N Stars and Stellar Evolution Super GUT Einstein s dream was to unite all four forces 4 Gravity as a Force Controls the Universe on large scales Inverse square law Gravity gets weaker as separation increases 1 FoC Z Central force gravitational force from a body of mass M is equivalent to the force if all of the mass were concentrated at the center Kepler s laws describing orbits give relation between mass and orbit for planet and sun or for 2 stars in orbit a3 lt semi major axis in AU m1 F m2 p2 lt period in years masses in solar units Escape velocity can an object escape the gravitational pull of another object rocket to the stars Answer only if it has more kinetic than potential energy If it does we say its velocity is greater than the escape velocity e g vesC from earth 2 ll kmsec Tidal force a difference in gravitational force from one part of an object to another due to their lying at different distances from a body exerting a gravitational force Tidal force is simply a difference between the effective gravitational force at two different positions distances from a body M position 1 position 2 Q Q equivalent objects 4 R d bl mass m The gravitational force at point 1 is GlVlm Fgmu R2 GlVlm Fgrav2 W Take the difference Fm1 Fgm Fgm2 algebra plus the fact that R gtgt d GMm 2d 2d X F rav R2 R g R 1998 Harriet L Dinerstein Astronomy 309N Stars and Stellar Evolution Since d is small compared to d the tidal force is small compared to Egmv but notice that it varies more rapidly with overall distance R than F grav F l grav X F Ftidal X E C THE NATURE OF MATTER AND LIGHT 1 Structure of Matter Nuclei of dimension about 10 13cm contain protons and neutrons 0 charge both belonging to the family of baryons During nuclear reactions the total of baryons is conserved as is the total net charge Electrons orbit or surround the nuclei at about lO39Scm electrons and neutrons belong to the lepton family Quantum theory says electron properties are guantized Bohr model modern theory electron orbitals old theory or probability distributions electrons dwell in discrete orbits at fixed radii electrons fill a certain volume of they jump to a higher or lower orbit by space within an atom but still have absorbing or emitting a photon quantum exactly defined energies of light energy 2 Nature of Light waveparticle duality Light as a wave lt 9 a 9 wavelength in A um cm etc f cyclessecond Hertz HZ M c where c 30 x1010cm Light as a particle Each photon has energy E hf where h Planck s constant 2 663 x 103927 erg gtlt sec Note This formula implicitly treats light as both wave and particle at the same time 1998 Harriet L Dinerstein Astronomy 309N Stars and Stellar Evolution The electromagnetic e m for short spectrum different regimes require different methods to study 10 5A 01 A 103 A 104 A lmm lOcm y rays X rays Ultra lnfra Micro Radio Violet red wave 9 a Visible uneven scale Doppler Effect A change in the apparentwavelength and frequency of light or other waves caused by relative motion of the source and receiver Motion apart a redshift stretches the wavecrests Motion towards blueshift crowds them together 3 Interaction of Light and Matter Matter absorbs and emits light e m radiation The nature of the spectrum which is produced depends upon the physical conditions a Kirchoff s Laws 1 Hot dense objects produce continuous blackbody spectra 2 Hot diffuse gases produce bright lines 3 Cool diffuse gases produce dark or absorption lines 1 The curve plot of energy vs wavelength has a distinct shape described by the Planck formula This is energy per unit area b Blackbody Spectra T E Aa 2 The total energy per unit area emitted by a blackbody all A s increases as T4 3 The wavelength of brightest emission varies inversely with temperature 9 Peak cc T l Hotter objects are bluer cEmission Line and Absogption Line Spectra both simply involve an an electron jumping between energy levels as mentioned before 1998 Harriet L Dinerstein Astronomy 309N Stars and Stellar Evolution Types of Spectra amp Examples in Astronomy 1 Blackbody spectra asteroids amp rocky planets or moons except for re ected sunlight stars approximately also have dark or absorption lines denser stars are closer to blackbodies iewhite dwarfs 2 Emission line spectra low density gas irradiated by hot stars eg the Great Nebula in Orion 3 Absorption line spectra starlight after passing through the thin upper layers or stellar atmosphere Spectra will tell you about 1 Composition line spectra only pure blackbodies give no information on the constituents 2 Temperature easiest to get for blackbodies for nebulae with emission lines or stellar atmospheres the details of which lines are brightest or darkest can with some effort yield temperature 3 Velocity through the Doppler effect need line spectra Since each type of atom has its own unique set of electron energy levels E1 E2 E3etc each type of atom produces lines at specific frequencies such that E photon hf 2 E2 E1 etc By observing the pattern set of X s or f s of lines it produces one can fingerprint a particular element actually ion and identify it anywhere astronomers do this through spectroscopy 4 The Behavior of Matter in Bulk a Phases of matter solid liquid gas plasma the fourth phase is merely ionized gas Where the electrons are free removed from the nuclei Of these solids and liquids are relatively incompressible ordinary gas is highly compressible Oquot the ideal gas or perfect gas is one which obeys the rule P constant x where T 2 temperature P 2 pressure V volume per unit mass the inverse of V is mass per unit volume or density 1 P V Sometimes astronomers prefer to use number density the number of atoms per unit volume n which is related to mass density by p 2 nm Where m the mass per particle 1998 Harriet L Dinerstein Astronomy 309N Stars and Stellar Evolution Restating the ideal gas law we have P constant gtlt pT nkT where k 138 x 10 16 ergK 1 Boltmann s constant Most of the interiors of M stars are ideal gases More generally the relationship between pressure temperature and density P p T is called the equation of state The ideal gas law is only one example of such a relation c Degenerate gases have a different equation of state In a degenerate gas the very high density leads to a large quantum pressure which greatly exceeds the ordinary thermal pressure given by the ideal gas law Consider a fully ionized dense gas The free electrons not attached to nuclei behave in certain ways described by quantum theory They follow 1 The Heisenber Uncertaint Princi le says that it is not possible to determine both an electron s position and momentum simultaneously with infinitely great accuracy momentum p mv is related to energy Another way to say this is that if you specify the momentum exactly the position is indeterminate the electron can be anywhere within a cell of diameter d so it fills that cell region where the electron is likely to be found I lf ih E l 2 Pauli Exclusion Principle says that no two electrons can occupy exactly the same quantum state read have the same momentum Applying this inside atoms you can only have two electrons one of each of two kinds of spin in each orbital Add another electron and it must go into the next higher level or orbit The periodic table of elements results from this rule Applying the exclusion principle to a degenerate gas as you keep packing in more and more electrons they must have greater and greater momenta By the time the spheres of the electrons touch the high average momentum means that they push on each other very hard constituting a large pressure The crucial thing about degeneracy pressure is that it depends only on density p temperature in the ordinary sense is irrelevant This 1998 Harriet L Dinerstein Astronomy 309N Stars and Stellar Evolution 2 2e Review of Basic Concepts Scientific Measurements 0 Scienti c Measurements 0 Scienti c Notation the number part 4 x 105 Q Matter In Motion P 23 X 10397 0 Structure of Matter 4 20 x 10 Q Messages of Light g 739 1 1 2 2e Proportionality A is to B Exponential Proportionality 0 Direct proportionality G Take a quantity to an exponential power eg distance velocity x time symbolically eg P2ltxa3 E Q Exponential proportionality can be fractional eg L 0 m35 eg velocity distance time symbolically r m ilk XL 0 Inverse proportionality 2 r XLgk Ar Units of Measurement Matter in Motion 0 Dimensions Length Mass Time C3 Position distance from reference point O Star dard 0 Speed length travelled per unit time cgs system 7 7 7 0 Natural or 0 Velocity rate ofchangein position convenient 7 7 2 units a O Accleration rate of change of velogfkty XL 51 75 InClass Notes Quantities of Motion FORCE MOMENTUM ENERGY Directional Vel or accel Expression 7 90505 DinersteinAst309N 8 2 Fundamental Forces O Gravity O Electromagnetic O Strong nuclear 0 Weak nuclear 39 X Newton s Law of Gravity d 2 an mC ass Nate gi a D mm 1 mm 11 lt51 72139 Gravity vs EM force Properties of Gravity T Inverse square law O Inverse square law gravitational Acts on Acts on force falls off Always attracts Attracts or repels 0 Escape veIOCIty depends on mass effect effect and O Tidal force difference in Dominates large scale Special situations x 7h at two different mags lt9 a 90605 Dinerstein Ast 309N 14 23 r 7quot gt3gt quotquot Forms of Energy Conservation of Energy Potential energy Q Energy can be converted from one form to another KInetIc Thermal O The total amount of energy sum of energy of all kinds remains constant 0000 Chemical it Electromagnetic r 23gt Momentum the third property 0 Forms Linear straight line v Angular of rotation Angular momentum the momentum involved in 1 Conservation of Momentum No change in velocity speed direction or both unless which causes an acceleration Conservation of angular momen um makes collapsing objects i z X Structure of Matter Subatomic Particles 0 Massive particles baryons eg protons neutrons 7 O Lighter particles leptons eg electrons neutrinos 7 x Matter is made of Atoms Nucleus electrons protons neutrons 90 a D 9mm Dn t mrlkstm m atomic number 1 atomic mass number 1 Helium atomic number 2 atomic mass number 4 r aiD 90605 Dinerstein Ast 309N 22 atomic mass number 2 The particles in the nucleus determine the element amp the isotope Jamirimmme number3961 ms 8mm 8 sfnumbstigui c mottois nwbhis Hydrogen 0H Heilum 14 Durban i9 cin nr nnmnm r mm 39uith p i mom mass number x a39a39nic mass 10th 4 mm mm ma 7 7 u eiecimni 1 eectvmsi is Sign The Huntsmi eiecmns In a neuuai am equals its atomic number Isulnpcs of Carbon Cnmmri c hnnri rehorrid WC WC HE lSpcicrs Emmians ismans 7neumns r mm Emums k Different Isotopes dim awen eieme ame nemiw he 5 nhmbarvi prams mimeem nu bersai netirons aiD 90605 Dinerstein Ast 309N 39 24 Periodic Table of the Elemenls atomic number protons What if an electron is removed ion has an 39 atomic elech39lc charge number 2 3 He1 atomic mass no protons neumk X ammic mass number 4 3 23gt an at 1 an e l tx it i Structure of Matter Atoms lanlaSS Notes O Nucleus protons neutrons 2 0 Electrons in fixed orbitslorbital clouds stay in orjump between orb39 a gt 317 c Wu 1 mm o Structure of Atoms xv Structure of Matter Atoms 53gt A Short Hist of antimatter O Opposite charge but same mass etc 0 Antielectron positron predmted by Dxra 1933 Nube F39qu measured by Andersun 183B pnze O Antiproton detected in 1 so Eievat 9 5 run pamde acceharatur LEL i X Creation of aLt39 hydrogen O Antihydrogen atoms created in 1995 m 2cm 2 Expe Armprutun Dee mpunance Hments usmg CERN S Eheratur made ml of aan if
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