Universe Eighth Edition Universe Roger A. Freedman William J. Kaufmann III CHAPTER 17 The Nature of Stars CHAPTER 17 The Nature of Stars

M 39 is an Open or Galactic Cluster

The distance (d) to a star can be determined from a measurement of the star’s parallax (p). Review of Previously Covered Concepts

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 = arcsec, d = 1/p = 1.3 pc Barnard’s Star: p = arcsec, d = 1/p = 1.83 pc Sirius A/B : p = arcsec, d = 1/p = 2.64 pc 1 pc = 206,265 AU = 3.26 LY

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. Review of Previously Covered Concepts

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. As you get farther and farther away from a star, it appears to get dimmer. Luminosity, L, doesn’t change Luminosity, L, doesn’t change Apparent brightness, b, does change following the inverse square law for distance. Apparent brightness, b, does change following the inverse square law for distance. b = L / (4  d 2 )

A star’s luminosity can be determined from its apparent brightness if its distance is known: 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 If a star’s distance is known, its luminosity can be determined from its brightness.

Example: The Sun d = 1 AU = 1.5  m b  = 1370 W/m 2 (Solar Constant) L  = 4  d 2 b  =   m  10 3 W/m 2 L  = 3.87  W

Example:  Eridani d = 3.22 pc = 3.22  206,265 AU = 6.65  10 5 AU b = 6.73  b  L/L  = (6.65  10 5 )  = 0.3  Eri has a luminosity equal to 30% of the solar luminosity.

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). Review of Previously Covered Concepts

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 Today we will learn

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

“main sequence”

More complete mapping of stars onto the H-R Diagram

Stefan-Boltzmann law relates a star’s energy output, called L UMINOSITY, to its temperature and size. L UMINOSITY = 4  R 2  T 4 L UMINOSITY is measured in joules per square meter of a surface per second and  = 5.67 X W m -2 K -4 Small stars will have low luminosities unless they are very hot. 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. Stars with low surface temperatures must be very large in order to have large luminosities. Stars come in a wide variety of sizes

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. 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. 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. 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 Main sequence stars Stars in hydrostatic equilibrium found on a line from the upper left to the lower right. Stars in hydrostatic equilibrium found on a line from the upper left to the lower right. Hotter is brighter Hotter is brighter Cooler is dimmer Cooler is dimmer Red Dwarfs (on MS) & Brown Dwarfs (not on MS): lower right corner (small, dim, and cool) Red Dwarfs (on MS) & Brown Dwarfs (not on MS): lower right corner (small, dim, and cool) Red giant stars Red giant stars Upper right hand corner (big, bright, and cool) Upper right hand corner (big, bright, and cool) White dwarf stars White dwarf stars Lower left hand corner (small, dim, and hot) 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