1. Discovering the Universe Eighth Edition Discovering the Universe Eighth Edition Neil F. Comins William J. Kaufmann III CHAPTER 11 Characterizing Stars CHAPTER 11 Characterizing Stars

2. Using Parallax to Determine Distance Our eyes change the angle between their lines of sight as we look at things that are different distances away. Our eyes are adjusting for the parallax of the things we see. This change helps our brains determine the distances to objects and is analogous to how astronomers determine the distance to objects in space.

3. Using Parallax to Determine Distance A nearby star appears to shift its position against the background of distant stars. The star’s parallax angle (p) is equal to the angle between the Sun and Earth, as seen from the star. The closer the star is to us, the greater the parallax angle p. The distance to the star (in parsecs) is found by taking the inverse of the parallax angle p (in arcseconds), d = 1/p.

4. Parallax Equation Distance (in parsecs) = 1/parallax angle (arcseconds) Distance (in parsecs) = 1/parallax angle (arcseconds) Or: D = 1/p Or: D = 1/p

5. Star Brightness Apparent Magnitude (m) Apparent Magnitude (m) -How bright a star appears to be -How bright a star appears to be -Lower magnitude number = brightest stars -Lower magnitude number = brightest stars -Higher magnitude number = dimmer -Higher magnitude number = dimmer

6. Apparent Magnitude Scale Several stars in and around the constellation Orion labeled with their names and apparent magnitudes. Astronomers denote the brightnesses of objects in the sky by apparent magnitudes. Stars visible to the naked eye have magnitudes between m = –1.44 and about m = +6.

7. Star Brightness Does apparent magnitude really tell us how bright a star actually is? Does apparent magnitude really tell us how bright a star actually is? Answer: No Apparent magnitude is dependant on how far away stars are Apparent magnitude is dependant on how far away stars are

8. The same amount of radiation from a light source must illuminate an ever-increasing area as the distance from the light source increases. The decrease in brightness follows the inverse-square law, which means, for example, that tripling the distance decreases the brightness by a factor of 9. The Inverse-Square Law

9. The car is seen at distances of 10 m, 20 m, and 30 m, showing the effect described in the previous image.

10. Absolute Magnitude Absolute Magnitude (M)- Describes the true brightness of a star no matter the distance -absolute magnitude describes the brightness of stars if they were moved to the standard distance of 10 pc -Range from -10 for brightest stars and +17 for the dimmest -allows astronomers to compare energy outputs of stars

11. Absolute Magnitude So, a star with the apparent magnitude = absolute magnitude would be at a distance of 10 parsecs.

12. Luminosity – describes the total energy output by stars Luminosity – describes the total energy output by stars Luminosity units are Watts (J/sec) Luminosity uses the sun as a comparison -Sun Luminosity (1 L Θ )= 400 x 10 24 W - A luminosity of 2 L Θ would have twice the total energy output - A luminosity of 2 L Θ would have twice the total energy output **Luminosity is also dependent on the size of the star

13. GO TO EM Spectrum!

14. Temperature and Color This beautiful Hubble Space Telescope image shows the variety of colors of stars. **(see class action UNL light module)

15. Temperature and Color The range of visible wavelengths is indicated. Where the peak of a star’s intensity curve lies relative to the visible light band determines the apparent color of its visible light.

16. Stellar Classification ClassificationTemperature Max Wavelength Color O040,000 K72.5 nmBlue B020,000 K145 nmLight Blue A010,000 K290 nmWhite F07,500 K387 nmYellow-White G05,500 K527 nmYellow K04,000 K725 nmOrange M03,000 K966 nmRed-Orange *Stars are classified based on their temperature and color: Oh Be A Fine Girl and Kiss Me *Each letter class has 10 subclasses (0-10 based on temperature) http://astro.unl.edu/naap/hr/hr.html

17. A Hertzsprung-Russell (H-R) Diagram

18. Types of Stars Determined by size Determined by size Dwarf ~20,000 mi diameter Sun ~800,000 mi diameter Giant ~6,000,000 mi diameter Supergiant ~500,000,000 mi diameter

19. A Hertzsprung-Russell Diagram

21. The Types of Stars and Their Sizes

22. The Mass-Luminosity Relation On this H-R diagram, each dot represents a main- sequence star. The number next to each dot is the mass of that star in solar masses (M). As you move up the main sequence from the lower right to the upper left, the mass, luminosity, and surface temperature of main- sequence stars all increase.

23. Summary of Key Ideas

24. Magnitude Scales Determining stellar distances from Earth is the first step to understanding the nature of the stars. Distances to the nearer stars can be determined by stellar parallax, which is the apparent shift of a star’s location against the background stars while Earth moves along its orbit around the Sun. The distances to more remote stars are determined using spectroscopic parallax. Determining stellar distances from Earth is the first step to understanding the nature of the stars. Distances to the nearer stars can be determined by stellar parallax, which is the apparent shift of a star’s location against the background stars while Earth moves along its orbit around the Sun. The distances to more remote stars are determined using spectroscopic parallax. The apparent magnitude of a star, denoted m, is a measure of how bright the star appears to Earth-based observers. The absolute magnitude of a star, denoted M, is a measure of the star’s true brightness and is directly related to the star’s energy output, or luminosity. The apparent magnitude of a star, denoted m, is a measure of how bright the star appears to Earth-based observers. The absolute magnitude of a star, denoted M, is a measure of the star’s true brightness and is directly related to the star’s energy output, or luminosity.

25. Magnitude Scales The absolute magnitude of a star is the apparent magnitude it would have if viewed from a distance of 10 pc. Absolute magnitudes can be calculated from the star’s apparent magnitude and distance. The absolute magnitude of a star is the apparent magnitude it would have if viewed from a distance of 10 pc. Absolute magnitudes can be calculated from the star’s apparent magnitude and distance. The luminosity of a star is the amount of energy emitted by it each second. The luminosity of a star is the amount of energy emitted by it each second.

26. The Temperatures of Stars Stellar temperatures can be determined from stars’ colors or stellar spectra. Stellar temperatures can be determined from stars’ colors or stellar spectra. Stars are classified into spectral types (O, B, A, F, G, K, and M) based on their spectra or, equivalently, their surface temperatures. Stars are classified into spectral types (O, B, A, F, G, K, and M) based on their spectra or, equivalently, their surface temperatures.

27. Types of Stars The Hertzsprung-Russell (H-R) diagram is a graph on which luminosities of stars are plotted against their spectral types (or, equivalently, their absolute magnitudes are plotted against surface temperatures). The Hertzsprung-Russell (H-R) diagram is a graph on which luminosities of stars are plotted against their spectral types (or, equivalently, their absolute magnitudes are plotted against surface temperatures). The H-R diagram reveals the existence of four major groupings of stars: main-sequence stars, giants, supergiants, and white dwarfs. The H-R diagram reveals the existence of four major groupings of stars: main-sequence stars, giants, supergiants, and white dwarfs. The mass-luminosity relation expresses a direct correlation between a main-sequence star’s mass and the total energy it emits. The mass-luminosity relation expresses a direct correlation between a main-sequence star’s mass and the total energy it emits. Distances to stars can be determined using their spectral types and luminosity classes. Distances to stars can be determined using their spectral types and luminosity classes.

28. Stellar Masses Binary stars are surprisingly common. Those that can be resolved into two distinct star images (even if it takes a telescope to do this) are called visual binaries. Binary stars are surprisingly common. Those that can be resolved into two distinct star images (even if it takes a telescope to do this) are called visual binaries. The masses of the two stars in a binary system can be computed from measurements of the orbital period and orbital dimensions of the system. The masses of the two stars in a binary system can be computed from measurements of the orbital period and orbital dimensions of the system. Some binaries can be detected and analyzed, even though the system may be so distant (or the two stars so close together) that the two star images cannot be resolved with a telescope. Some binaries can be detected and analyzed, even though the system may be so distant (or the two stars so close together) that the two star images cannot be resolved with a telescope.

29. Stellar Masses A spectroscopic binary is a system detected from the periodic shift of its spectral lines. This shift is caused by the Doppler effect as the orbits of the stars carry them alternately toward and away from Earth. A spectroscopic binary is a system detected from the periodic shift of its spectral lines. This shift is caused by the Doppler effect as the orbits of the stars carry them alternately toward and away from Earth. An eclipsing binary is a system whose orbits are viewed nearly edge-on from Earth, so that one star periodically eclipses the other. Detailed information about the stars in an eclipsing binary can be obtained by studying its light curve. An eclipsing binary is a system whose orbits are viewed nearly edge-on from Earth, so that one star periodically eclipses the other. Detailed information about the stars in an eclipsing binary can be obtained by studying its light curve. Mass transfer occurs between binary stars that are close together. Mass transfer occurs between binary stars that are close together.

30. Key Terms absolute magnitude apparent magnitude binary star center of mass close binary eclipsing binary giant star Hertzsprung-Russell (H-R) diagram initial mass function inverse-square law light curve luminosity luminosity class main sequence main-sequence star mass-luminosity relation OBAFGKM sequence optical double photometry radial-velocity curve red giant spectral types spectroscopic binary spectroscopic parallax stellar evolution stellar parallax stellar spectroscopy supergiant visual binary white dwarf

31. WHAT DID YOU THINK? How near to us is the closest star other than the Sun? How near to us is the closest star other than the Sun? Proxima Centauri is about 25 trillion mi (40 trillion km) away. Light from there will take about 4 years to reach Earth. Proxima Centauri is about 25 trillion mi (40 trillion km) away. Light from there will take about 4 years to reach Earth.

32. WHAT DID YOU THINK? How luminous is the Sun compared with other stars? How luminous is the Sun compared with other stars? The most luminous stars are about a million times brighter, and the least luminous stars are about a hundred thousand times dimmer than the Sun. The most luminous stars are about a million times brighter, and the least luminous stars are about a hundred thousand times dimmer than the Sun.

33. WHAT DID YOU THINK? What colors are stars, and why do they have these colors? What colors are stars, and why do they have these colors? Stars are found in a wide range of colors, from red through violet as well as white. They have these colors because they have different temperatures. Stars are found in a wide range of colors, from red through violet as well as white. They have these colors because they have different temperatures.

34. WHAT DID YOU THINK? Are brighter stars hotter than dimmer stars? Are brighter stars hotter than dimmer stars? Not necessarily. Many brighter stars, such as red giants, are cooler but larger, than hotter, dimmer stars, such as white dwarfs. Not necessarily. Many brighter stars, such as red giants, are cooler but larger, than hotter, dimmer stars, such as white dwarfs.

35. WHAT DID YOU THINK? Compared to the Sun, what sizes are other stars? Compared to the Sun, what sizes are other stars? Stars range from more than 1000 times the Sun’s diameter to less than 1/100 the Sun’s diameter. Stars range from more than 1000 times the Sun’s diameter to less than 1/100 the Sun’s diameter.

36. WHAT DID YOU THINK? Are most stars isolated from other stars, as the Sun is? Are most stars isolated from other stars, as the Sun is? No. In the vicinity of the Sun, one-third of the stars are found in pairs or larger groups. No. In the vicinity of the Sun, one-third of the stars are found in pairs or larger groups.