Roger A Freedman William J Kaufmann III Universe Eighth Eighth Edition Edition CHAPTER 17 The Nature of Stars M 39 is an Open or Galactic Cluster Review of Previously Covered Concepts The distance d to a star can be determined from a measurement of the star s parallax p Stellar Parallax As Earth moves from one side of the Sun to the other a nearby star will seem to change its position relative to the distant background stars d 1 p d distance to nearby star in parsecs p parallax angle of that star in arcseconds Some Nearby Stars Proxima Centauri p 0 772 arcsec d 1 p 1 3 pc Barnard s Star p 0 545 arcsec d 1 p 1 83 pc Sirius A B p 0 379 arcsec d 1 p 2 64 pc 1 pc 206 265 AU 3 26 LY Review of Previously Covered Concepts The distance d to a star can be determined from a measurement of the star s parallax p The intrinsic brightness or luminosity L of a star can be determined from a measurement of the star s apparent brightness b and a knowledge of the star s distance If a star s distance is known its luminosity can be determined from its brightness As you get farther and farther away from a star it appears to get dimmer Luminosity L doesn t change Apparent brightness b does change following the inverse square law for distance b L 4 d2 If a star s distance is known its luminosity can be determined from its brightness A star s luminosity can be determined from its apparent brightness if its distance is known L 4 d 2 b L 4 d 2 b L L d d 2 b b Where L the Sun s luminosity Example The Sun d 1 AU 1 5 1011 m b 1370 W m2 Solar Constant L 4 d2 b 1 256 101 2 25 1022 m2 1 37 103 W m2 L 3 87 1026 W Example Eridani d 3 22 pc 3 22 206 265 AU 6 65 105 AU b 6 73 10 13 b L L 6 65 105 2 6 73 10 13 0 3 Eri has a luminosity equal to 30 of the solar luminosity Review of Previously Covered Concepts The distance d to a star can be determined from a measurement of the star s parallax p The intrinsic brightness or luminosity L of a star can be determined from a measurement of the star s apparent brightness b and a knowledge of the star s distance The surface temperature T of a star can be determined from a measurement of the star s color or spectral type Today we will learn 17 7 How H R diagrams summarize our knowledge of the stars 17 6 How stars come in a wide variety of sizes 17 8 How we can deduce a star s size from its spectrum Let s pause to examine the spread of L and T values among the stars that are nearest to us Appendix 4 Plot L vs T for 27 Nearest Stars Data drawn from Appendix 4 of the textbook L and T appear to be Correlated Nearest Stars L and T appear to be Correlated A few of the brightest stars in the night sky Hertzsprung Russell H R Diagram Hertzsprung Russell H R Diagram m ai n se qu en c e More complete mapping of stars onto the H R Diagram Stars come in a wide variety of sizes Stefan Boltzmann law relates a star s energy output called LUMINOSITY to its temperature and size LUMINOSITY 4 R2 T4 LUMINOSITY is measured in joules per square meter of a surface per second and 5 67 X 10 8 W m 2 K 4 Small stars will have low luminosities unless they are very hot Stars with low surface temperatures must be very large in order to have large luminosities Determining the Sizes of Stars from an H R Diagram Main sequence stars are found in a band from the upper left to the lower right Giant and supergiant stars are found in the upper right corner Tiny white dwarf stars are found in the lower left corner of the HR diagram Hertzsprung Russell H R diagrams reveal the different kinds of stars Main sequence stars Red giant stars Stars in hydrostatic equilibrium found on a line from the upper left to the lower right Hotter is brighter Cooler is dimmer Red Dwarfs on MS Brown Dwarfs not on MS lower right corner small dim and cool Upper right hand corner big bright and cool White dwarf stars Lower left hand corner small dim and hot Details of a star s spectrum reveal whether it is a giant a white dwarf or a main sequence star Both of these stars are spectral class B8 However star a is a luminous super giant and star b is a typical main sequence star Notice how the hydrogen absorption lines for the more luminous stars are narrower LUMINOSITY CLASS Based on the width of spectral lines it is possible to tell whether the star is a supergiant a giant a main sequence star or a white dwarf These define the luminosity classes shown on the left occupying distinct regions on the HR diagram The complete spectral type of the Sun is G2 V The G2 part tells us Teff the V part tells us to which sequence or luminosity class the star belongs Example M5 III is a red giant with Teff 3500K M 0 or L 100 Lsun HR Diagram This template will be used in the upcoming test Please become familiar with it We will do a few examples in class of how to read off the temperature luminosity and size of a star given a full spectral type HR Diagram I expect you to know which of the gray sequences is which luminosity class From top to bottom Ia luminous supergiants Ib supergiants III giants V main sequence Examples G2V The Sun M5III B4Ib M5Ia