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

17-1 How we can measure the distances to the stars Box 17-1 Stellar Motions 17-2 How we measure a star’s brightness and luminosity and depending on time available 17-3 The magnitude scale for brightness and luminosity Today, we will learn

The brightness of a star is not a good indicator of distance. The brightness of a star is not a good indicator of distance. e.g., Polaris is closer than Betelgeuse but Betelgeuse appears brighter. Distances to nearby stars can be measured using parallax (see Section 4-3, Fig. 4-7, Tycho Brahe). Distances to nearby stars can be measured using parallax (see Section 4-3, Fig. 4-7, Tycho Brahe). Parallax is the apparent change in the position of an object due to a change in observing position. Careful measurements of the parallaxes of stars reveal their distances.

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

Parsec Is the distance corresponding to a Parallax of one arc second 206, arc sec So, 1 pc = 206,265 AU 1 arc sec = 1 degree /3,600

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

Stellar Motions The Doppler Effect reveals the radial velocity

Stellar Motions The rate of change in position on the sky is the proper motion. If we know the distance we can calculate the tangential velocity.

Example: Barnard’s Star A certain iron line of wavelength 0 = nm is observed in the spectrum at a wavelength  = nm. Using the Doppler formula  / 0 = (  0 )/ 0 =( – )/ =  So the radial velocity is v r =  c =  111 km/s The negative sign means this star is approaching us.

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

17-2 How we measure a star’s brightness and calculate its luminosity knowing the distance The magnitude scale for brightness and luminosity. Introduce the distance modulus. Today, we will learn

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.

Luminosity Function As stars go, our Sun is neither extremely luminous nor extremely dim. It is somewhat more luminous than most nearby stars – of the 30 stars within 4 pc, only three have a greater luminosity. 1 L  = 3.86 X W

Historically, the apparent magnitude scale for naked eye stars, runs from 1 (brightest) to 6 (dimmest). Historically, the apparent magnitude scale for naked eye stars, runs from 1 (brightest) to 6 (dimmest). Today, the apparent magnitude scale extends into the negative numbers for really bright objects and into the 20s and 30s for really dim objects. Today, the apparent magnitude scale extends into the negative numbers for really bright objects and into the 20s and 30s for really dim objects. Absolute magnitude, on the other hand is how bright a star would look if it were 10 pc away. Absolute magnitude, on the other hand is how bright a star would look if it were 10 pc away. Astronomers often use the magnitude scale to denote brightness.

Modern Magnitude Scale     2.512=(2.512) 5 =100 A star of magnitude 4.2 is times brighter than another star of magnitude st magnitude are 100 times brighter than 6 th magnitude A star of magnitude 3 is dimmer than 2 by b 3 = b 2 /2.512 A star of magnitude 7 is brighter than a 9 th mag star by b 7 = b 9 (2.512) 2 = 6.31

Astronomers often use the magnitude scale to denote brightness.

Apparent Magnitude m Two stars of magnitudes m 1 and m 2 have brightness ratio b 2 /b 1 = (2.512) m 1 -m 2 Nova Cygni 1975 brightened by 13 magnitudes in two days: it went from m 1 = 15 to m 2 = 2, so b 2 /b 1 = (2.512) m 1 -m 2 = 185,000. If a star of apparent magnitude m were to be moved to a new location 10 times farther away, its brightness would decrease by a factor of 100. Therefore its new apparent magnitude would be m + 5.

Absolute Magnitude M M is the apparent magnitude a star would have at a distance of 10 pc. Example: the sun at 10 pc b/ b  = 1/ (2,062,650) 2 = 2.35  = (2.512) M M =  5 For any star actually 10 pc distant, m = M Any star at 100 pc appears 100 times fainter than at 10 pc Therefore m = M + 5 Any star at 1000 pc appears 100 times fainter than at 100 pc Therefore m = M + 10

Distance Modulus m  M This concept enables a distance determination if you know the absolute magnitude. The apparent magnitude is always determined from observation. d = 10 pc 10 (m  M)/5 m  M d (pc)

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.

If a star’s luminosity is known, its distance can be determined from its brightness. A star’s distance can be determined from its apparent brightness if its luminosity is known: A star’s distance can be determined from its apparent brightness if its luminosity is known: L/L  = (d/d  ) 2  (b/b  ) Where L  = the Sun’s luminosity ( d/d  ) 2 = (L/L  ) / (b/b  ) ( d/d  ) 2 = (L/L  ) / (b/b  ) And finally (see also Box 17-2)   

17-4 How a star’s color indicates its temperature 17-5 How a star’s spectrum reveals its chemical composition 17-6 How we can determine the sizes of stars Today, we will learn

The solar spectrum at high dispersion shows hundreds of absorption lines corresponding to hydrogen and many other elements.

The spectra of stars reveal their chemical compositions as well as surface temperatures. In the late 19 th Century, spectra were obtained for hundreds of thousands of stars. In the late 19 th Century, spectra were obtained for hundreds of thousands of stars. These stellar spectra were grouped into a classification scheme of spectral types A through O by a team at Harvard. These stellar spectra were grouped into a classification scheme of spectral types A through O by a team at Harvard. Today we recognize the spectral types O, B, A, F, G, K, M, L and T, running from hottest to coolest.

O B A F G K M L T O B A F G K M L T hottest to coolest hottest to coolest bluish to reddish bluish to reddish Further refined by attaching an integer, for example: F0, F1, F2, F3 … F9 where F1 is hotter than F3 Further refined by attaching an integer, for example: F0, F1, F2, F3 … F9 where F1 is hotter than F3 An important sequence to remember: An important sequence to remember: Oh Be a Fine Girl (or Guy), Kiss Me Lovingly, Tenderly Oh Be a Fine Girl (or Guy), Kiss Me Lovingly, Tenderly The spectra of stars reveal their chemical compositions as well as surface temperatures.

Cecilia Payne-Gaposchkin & Meghnad Saha In her doctoral dissertation (1925) CPG demonstrated that the spectral sequence OBAFGKM is the result of the emission and absorption by gas of “cosmic” composition with decreasing temperature. Saha’s Equation (1920) CPG at Harvard

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

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)

Determining the Sizes of Stars from an HR 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.

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

Double star – a pair of stars located at nearly the same position in the night sky. Double star – a pair of stars located at nearly the same position in the night sky. Optical double stars – stars that lie along the same line of sight, but are not close to one another. Optical double stars – stars that lie along the same line of sight, but are not close to one another. Binary stars, or binaries – stars that are gravitationally bound and orbit one another. Binary stars, or binaries – stars that are gravitationally bound and orbit one another. Visual binary – binaries that can be resolved Visual binary – binaries that can be resolved Spectroscopic binary – binaries that can only be detected by seeing two sets of lines in their spectra Spectroscopic binary – binaries that can only be detected by seeing two sets of lines in their spectra Eclipsing binary – binaries that cross one in front of the other. Eclipsing binary – binaries that cross one in front of the other. Binary star systems provide crucial information about stellar masses.

Binary Star Krüger 60 (upper left hand corner) About half of the stars visible in the night sky are part of multiple-star systems.

 izar   UMa or Zeta-one Ursae Majoris, a~0.01”, P = 20.5 d Courtesy: Navy Prototype Optical Interferometer

Spectroscopy makes it possible to study binary systems in which the two stars are close together.  Ari

Light curves of eclipsing binaries provide detailed information about the two stars: Sizes, effective temperatures, shapes, etc

Light curves of eclipsing binaries provide detailed information about the two stars.

NN Ser ESO

Discussion of Problem 66

Key Ideas Measuring Distances to Nearby Stars: Distances to the nearer stars can be determined by parallax, the apparent shift of a star against the background stars observed as the Earth moves along its orbit. Parallax measurements made from orbit, above the blurring effects of the atmosphere, are much more accurate than those made with Earth-based telescopes. Stellar parallaxes can only be measured for stars within a few hundred parsecs. The Inverse-Square Law: A star’s luminosity (total light output), apparent brightness, and distance from the Earth are related by the inverse-square law. If any two of these quantities are known, the third can be calculated.

Key Ideas The Population of Stars: Stars of relatively low luminosity are more common than more luminous stars. Our own Sun is a rather average star of intermediate luminosity. The Population of Stars: Stars of relatively low luminosity are more common than more luminous stars. Our own Sun is a rather average star of intermediate luminosity. The Magnitude Scale: The apparent magnitude scale is an alternative way to measure a star’s apparent brightness. The Magnitude Scale: The apparent magnitude scale is an alternative way to measure a star’s apparent brightness. The absolute magnitude of a star is the apparent magnitude it would have if viewed from a distance of 10 parsecs. A version of the inverse-square law relates a star’s absolute magnitude, apparent magnitude, and distance. The absolute magnitude of a star is the apparent magnitude it would have if viewed from a distance of 10 parsecs. A version of the inverse-square law relates a star’s absolute magnitude, apparent magnitude, and distance.

Key Ideas Photometry and Color Ratios: Photometry measures the apparent brightness of a star. The color ratios of a star are the ratios of brightness values obtained through different standard filters, such as the U, B, and V filters. These ratios are a measure of the star’s surface temperature. Photometry and Color Ratios: Photometry measures the apparent brightness of a star. The color ratios of a star are the ratios of brightness values obtained through different standard filters, such as the U, B, and V filters. These ratios are a measure of the star’s surface temperature. Spectral Types: Stars are classified into spectral types (subdivisions of the spectral classes O, B, A, F, G, K, and M), based on the major patterns of spectral lines in their spectra. The spectral class and type of a star is directly related to its surface temperature: O stars are the hottest and M stars are the coolest. Spectral Types: Stars are classified into spectral types (subdivisions of the spectral classes O, B, A, F, G, K, and M), based on the major patterns of spectral lines in their spectra. The spectral class and type of a star is directly related to its surface temperature: O stars are the hottest and M stars are the coolest. Most brown dwarfs are in even cooler spectral classes called L and T. Unlike true stars, brown dwarfs are too small to sustain thermonuclear fusion. Most brown dwarfs are in even cooler spectral classes called L and T. Unlike true stars, brown dwarfs are too small to sustain thermonuclear fusion.

Key Ideas Hertzsprung-Russell Diagram: The Hertzsprung- Russell (H-R) diagram is a graph plotting the absolute magnitudes of stars against their spectral types—or, equivalently, their luminosities against surface temperatures. Hertzsprung-Russell Diagram: The Hertzsprung- Russell (H-R) diagram is a graph plotting the absolute magnitudes of stars against their spectral types—or, equivalently, their luminosities against surface temperatures. The positions on the H-R diagram of most stars are along the main sequence, a band that extends from high luminosity and high surface temperature to low luminosity and low surface temperature. The positions on the H-R diagram of most stars are along the main sequence, a band that extends from high luminosity and high surface temperature to low luminosity and low surface temperature.

Key Ideas On the H-R diagram, giant and supergiant stars lie above the main sequence, while white dwarfs are below the main sequence. On the H-R diagram, giant and supergiant stars lie above the main sequence, while white dwarfs are below the main sequence. By carefully examining a star’s spectral lines, astronomers can determine whether that star is a main- sequence star, giant, supergiant, or white dwarf. Using the H-R diagram and the inverse square law, the star’s luminosity and distance can be found without measuring its stellar parallax. By carefully examining a star’s spectral lines, astronomers can determine whether that star is a main- sequence star, giant, supergiant, or white dwarf. Using the H-R diagram and the inverse square law, the star’s luminosity and distance can be found without measuring its stellar parallax.

Key Ideas Binary Stars: Binary stars, in which two stars are held in orbit around each other by their mutual gravitational attraction, are surprisingly common. Those that can be resolved into two distinct star images by an Earth-based telescope are called visual binaries. Binary Stars: Binary stars, in which two stars are held in orbit around each other by their mutual gravitational attraction, are surprisingly common. Those that can be resolved into two distinct star images by an Earth-based telescope are called visual binaries. Each of the two stars in a binary system moves in an elliptical orbit about the center of mass of the system. Each of the two stars in a binary system moves in an elliptical orbit about the center of mass of the system. Binary stars are important because they allow astronomers to determine the masses of the two stars in a binary system. The masses can be computed from measurements of the orbital period and orbital dimensions of the system. Binary stars are important because they allow astronomers to determine the masses of the two stars in a binary system. The masses can be computed from measurements of the orbital period and orbital dimensions of the system.

Key Ideas Mass-Luminosity Relation for Main-Sequence Stars: Main-sequence stars are stars like the Sun but with different masses. The mass-luminosity relation expresses a direct correlation between mass and luminosity for main- sequence stars. The greater the mass of a main- sequence star, the greater its luminosity (and also the greater its radius and surface temperature).

Key Ideas Spectroscopic Observations of Binary Stars: 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. Spectroscopic Observations of Binary Stars: 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. A spectrum binary appears to be a single star but has a spectrum with the absorption lines for two distinctly different spectral types. A spectrum binary appears to be a single star but has a spectrum with the absorption lines for two distinctly different spectral types.

Key Ideas A spectroscopic binary has spectral lines that shift back and forth in wavelength. This is caused by the Doppler effect, as the orbits of the stars carry them first toward then away from the Earth. A spectroscopic binary has spectral lines that shift back and forth in wavelength. This is caused by the Doppler effect, as the orbits of the stars carry them first toward then away from the Earth. An eclipsing binary is a system whose orbits are viewed nearly edge-on from the Earth, so that one star periodically eclipses the other. Detailed information about the stars in an eclipsing binary can be obtained from a study of the binary’s radial velocity curve and its light curve. An eclipsing binary is a system whose orbits are viewed nearly edge-on from the Earth, so that one star periodically eclipses the other. Detailed information about the stars in an eclipsing binary can be obtained from a study of the binary’s radial velocity curve and its light curve.

17-7 How H-R diagrams summarize our knowledge of the stars 17-8 How we can deduce a star’s size from its spectrum 17-9 How we can use binary stars to measure the masses of stars How we can learn about binary stars in very close orbits What eclipsing binaries are and what they tell us about the sizes of stars Today we will learn