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Properties of Stars http://youtu.be/zaOPsmlJyw8 1 Lecture Learning goals: ! Explain what is meant by the inverse-square law and apply it to the measurements of light at different distances. ! Define apparent and absolute magnitudes. ! Explain what a “parsec” is and why it is convenient for astronomers in estimating distances and luminosities of stars. !Describe the methods used to determine the temperature, luminosity, and radius of a star. !State the “goldilocks” analogy for strengths of hydrogen lines in the spectra of stars OBAFGKM. 2 Inverse square law for light of light ! Explain what is meant by the inverse-square law and apply it to the measurements 3 at different distances. Brightness How the star looks to US HERE ON EARTH. L apparent brightness = 4 πD2 Each of these light bulbs will appear to be the same brightness. 1000 times farther away " 100 Watt 1 Watts 1000 Watt € 10 times farther away " 2 x farther away, 1/4 as bright 3 x farther away, 1/9 as bright 4 of light ! Explain what is meant by the inverse-square law and apply it to the measurements at different distances. Apparent Magnitude # Every 5 magnitudes difference means 100 x difference in brightness # One magnitude difference is 2.512 times in brightness. (2.5125 = 100) !Define apparent and absolute magnitudes. 5 When you see only “magnitude,” that means APPARENT magnitude. 1. The magnitude (m) of star A is 1, the magnitude (m) of star B is 6. How many times brighter is A than B? a) 5 b) 10 c) 100 d) 1000 2. m of star C is 12, m of star D is 2: How many times brighter is star D than star C? (Or, equally stated, how many times dimmer is star C than star D?) a) 10 • b) 24 c) 100 d) 10,000 The Sun is the brightest star in the sky, with an apparent magnitude of about -26.5 Sirius is next in line, with an apparent magnitude of -1.5; how many times brighter is the Sun than Sirius? a) 25 b) 28 c) 100,000 !Define apparent and absolute magnitudes. d) 10,000,000,000 6 Brightness: Magnitude • Some useful definitions: ▪ Brightness of a star is measured by logarithmic magnitude. => Brighter objects have a smaller magnitude. ▪ Apparent magnitude: how bright the star appears to us in the sky. m ▪ Absolute magnitude: how bright the star would be at a distance of 10 parsecs from us. M d is in parsecs !Define apparent and absolute magnitudes. PARSEC: Parallax ARc SECond A star having a parallax of 1 arc second is 1 parsec away 1 parsec (pc) = 3.26 light years 1 kiloparsec (1 kpc) = 1000 pc; 1 megaparsec (1 Mpc) = 1,000,000 pc Baseline is 1 Astronomical Unit ! Explain what a “parsec” is and why it is convenient for astronomers in estimating 8 distances and luminosities of stars. Continuous Spectrum - created by thermal radiator (blackbody radiation) Hotter stars look more blue-white than cooler stars because hot stars emit most of their light at shorter wavelengths. Star field in Sagittarius Wien’s Law 6 2.9 × 10 λ peak = nm T 6 2.9 × 10 T = K λ peak € 9 ! Describe the methods used to determine the temperature, luminosity, and radius of a star. http://stardate.org/radio/program/delta-lyrae 10 the words in the equation with the approical expressions for the Stefan-Boltzmann of a sphere, our equation for the luminoss like this: J J 4 ____ __ nosity ( ) = σT s (m s) 2 × 4πR2(m 2) : L = 4πR2 σT 4 J/s (W) Suppose w star in the con geuse (see the we know that 3500 K. Its di and its brightn times that of th telgeuse? Usin the following: onstants (4, π, and σ) do not change, the lur is proportional only to R2T 4. Make a star 3 nd its surface area becomes 32 = 9 times as times as much area to radiate, so there is 9 adiation. Make a star twice as hot, and each Describe the methods used to determine the temperature, luminosity, and radius of a star. ! RB __ = Understanding Our Universe, 1st Edition 4 Copyright © 2012 W. W. Norton & Company √ we know here on Earth applies to the rest of the solar system, the Galaxy, and the Universe. In this tutorial you will be led through the steps to understanding the Stefan-Boltzmann Law: The amount of energy put out per second (the number of watts) is proportional to the surface area of the sphere (4 pi times the radius squared) and the temperature raised to the 4th power. (The σ represents the −8 -2 -4 Stefan-Boltzmann constant, 5.67 ×10 W·m ·K .) L = 4" r 2! T 4 You are comparing the ability of a grouping of electric hot plates (shown below as burners on a “stove top”) of different sizes and temperatures to bring identical pots of water to a boil. The pots are all as large as the largest hot plate. The temperatures of the hot plates are coded: the lighter the shade of gray, the higher the temperature. High Medium Low 1. For each pair of hot plates (read horizontally), circle the one that will boil the water more quickly. Is there a set of burners for which there is no way to tell? If so, which ones? ! Describe the methods used to determine the temperature, luminosity, and radius of a star. The H-R Diagram 13 ! Describe the methods used to determine the temperature, luminosity, and radius of a star. H-R Diagram: O and M Stars ▪ On far left end of the main sequence are the O stars: hotter, larger, and more luminous than the Sun. • ▪ On far right end of the main sequence are the M stars: cooler, smaller, and fainter than the Sun. ! Describe the methods used to determine the temperature, luminosity, and radius of a star. Cool stars are red. Hot stars are blue. The H-R Diagram Hotter 107 0R Supergiants 105 100 –10 £ R£ –5 10 R 103 102 All stars with a radius of 1 R£ lie along this line. 1R 101 0.1 1 0.01 10–1 10–2 10 0.00 –3 10–4 10–5 1R MA IN £ £ Giants SE 0 QU EN CE R£ Sun +5 R£ White dwarfs +10 £ H-R diagrams are sometimes plotted with either spectral type or temperature. 40,000 30,000 20,000 +15 10,000 3000 2500 6000 Surface temperature (K) O5 B0 B5 A0 Spectral type F0 G0 K5 15 M5 ! Describe the methods used to determine the temperature, luminosity, and radius of a star. More luminous Visual luminosity relative to Sun 104 Absolute visual magnitude Simulation of the actual relative sizes of a giant star versus the Sun. 1,00 106 http://media.wwnorton.com/college/astronomy/animations/interactive/hrexplorer.html ! Describe the methods used to determine the temperature, luminosity, and radius of a star. ! Classify stars and organize this information. 1 Ångstrom = 10-10 meters Composition: Spectral Types Subclasses • ▪ Absorption lines depend primarily on temperature of photosphere. ▪ Full sequence for stars radiating mostly in the visible: OBAFGKM ▪ Each spectral type is broken down into 10: 0-9. => The Sun is type G2. ! Classify stars and organize this information. Composition: Emission • ▪ Emission: an electron emits a photon and drops to a lower energy state, losing energy. ▪ The photon’s energy is equal to the energy difference between the two levels. Composition: Absorption • ▪ Absorption: an electron absorbs the energy of a photon to jump to a higher energy level. ▪ The photon’s energy must be equal to the energy difference between the two levels. Composition: Absorption Lines • ▪ For stars, astronomers look at the dark absorption lines in stars’ spectra. ▪ These absorption lines help determine a star’s temperature, composition, density, pressure, and more. Sun (G2 V) as a Blackbody Radiator 22 !State the “goldilocks” analogy for strengths of hydrogen lines in the spectra of stars OBAFGKM. • Spectral type O stars are so hot, the photons so energetic that almost all of the hydrogen atoms are ionized. • Spectral type M stars are so cool, the photons do not have enough energy to excite the hydrogen electrons to the second energy level. • Spectral type A stars are just the right temperature that photons can excite electrons to second energy level where they can absorb photons of a range of energies Colors represent filter regions. U B V ! Classify stars and organize this information. R I U B V ! Classify stars and organize this information. R I U B V ! Classify stars and organize this information. R I U B V ! Classify stars and organize this information. R I U B V ! Classify stars and organize this information. R I U B V ! Classify stars and organize this information. R I U B V ! Classify stars and organize this information. R I !State the “goldilocks” analogy for strengths of hydrogen lines in the spectra of stars OBAFGKM. • Spectral type O stars are so hot, the photons so energetic that almost all of the hydrogen atoms are ionized. • Spectral type M stars are so cool, the photons do not have enough energy to excite the hydrogen electrons to the second energy level. • Spectral type A stars are just the right temperature that photons can excite electrons to second energy level where they can absorb photons of a range of energies Lecture Learning goals: ! Explain what is meant by the inverse-square law and apply it to the measurements of light at different distances. 34 ! Define apparent and absolute magnitudes. ! Explain what a “parsec” is and why it is convenient for astronomers in estimating distances and luminosities of stars. !Describe the methods used to determine the temperature, luminosity, and radius of a star. !State the “goldilocks” analogy for strengths of hydrogen lines in the spectra of stars OBAFGKM. • Spectral type O stars are so hot, the photons so energetic that almost all of the hydrogen atoms are ionized. • Spectral type M stars are so cool, the photons do not have enough energy to excite the hydrogen electrons to the second energy level. • Spectral type A stars are just the right temperature that photons can excite electrons to second energy level where they can absorb photons of a range of energies