Chapter 12: Characterizing Stars PDF

Discovering the Universe ELEVENTH EDITION Chapter 12 Characterizing Stars Copyright © 2019 by W. H. Freeman and Company In this chapter you will discover… (1 of 2) that the distances to many nearby stars can be measured directly, whereas th...

Discovering the Universe ELEVENTH EDITION Chapter 12 Characterizing Stars Copyright © 2019 by W. H. Freeman and Company In this chapter you will discover… (1 of 2) that the distances to many nearby stars can be measured directly, whereas the distances to farther ones are determined indirectly the observed properties of stars on which astronomers base their models of stellar evolution how astronomers analyze starlight to determine a star’s temperature and chemical composition In this chapter you will discover… (2 of 2) how the total energy emitted by stars and their surface temperatures are related the different classes of stars the variety and importance to astronomers of binary star systems how astronomers calculate stellar masses Using Parallax to Determine Distance (1 of 4)  Using Parallax to Determine Distance (2 of 4) a) and b) 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 distances to objects in space. Using Parallax to Determine Distance (3 of 4)  Using Parallax to Determine Distance (4 of 4) c) As Earth orbits the Sun, 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 stars on the scale of this drawing are shown much closer than they are in reality. If drawn to the correct scale, the closest star, other than the Sun, would be about 5 km (3.2 mi) away. d) 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.  Luminosity and Magnitude (1 of 2) The luminosity of a star is the amount of energy it emits each second. It is not the same as brightness, even though more luminous stars usually appear brighter. Greek astronomers, from Hipparchus in the second century B.C.E. to Ptolemy (90–168 C.E.) in the second century C.E., undertook the classification of stars strictly by evaluating how bright they appear to be relative to each other. The apparent magnitude of a star, denoted m, is a measure of how bright the star appears to Earth-based observers.  Luminosity and Magnitude (2 of 2) 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 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 from Earth. Apparent Magnitude Scale (1 of 2)  Apparent Magnitude Scale (2 of 2) a) Several stars in and around the constellation Orion, labeled with their names and apparent magnitudes. For a discussion of star names, see Guided Discovery: Star Names. b) Astronomers denote the brightnesses of objects in the sky by their apparent magnitudes. Stars visible to the naked eye have magnitudes between m = -1.44 (Sirius) and about m = +6.0. However, CCD (charge-coupled device) photography through the Hubble Space telescope or a large Earth-based telescope can reveal stars and other objects nearly as faint as magnitude m = +31.5. Note that Pluto's apparent magnitude varies from +13.7 to +16.3, depending on its distance from Earth. Its average apparent magnitude is +15.1. The Inverse-Square Law (1 of 4)  The Inverse-Square Law (2 of 4) a) 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 (3 of 4)  The Inverse-Square Law (4 of 4) b) The car is seen at distances of 10 m, 20 m, and 30 m, showing the effect described in part (a).  Radiation Laws Revisited Wien’s law states that the peak wavelength of radiation emitted by a blackbody is inversely proportional to its temperature—the higher its temperature, the shorter the peak wavelength. The intensities of radiation emitted at various wavelengths by a blackbody at a given temperature are shown as a blackbody curve. The Stefan-Boltzmann law shows that a hotter blackbody emits more radiation at every wavelength than does a cooler blackbody. It can be used to determine how much brighter (the luminosity) a hotter star is than a cooler one. Temperature and Color (1 of 2)  Temperature and Color (2 of 2) These diagrams show the relationship between the color of a star and its surface temperature. The intensity of light emitted by three stars is plotted against wavelength (compare with Figure 4-2). The range of visible wavelengths is indicated. The location of the peak of each star’s intensity curve, relative to the visible-light band, determines the apparent color of its visible light. The insets show stars of about these surface temperatures. Ultraviolet (UV) extends to 10 nm. See Figure 3-6 for more on wavelengths of the spectrum. The Spectra of Stars with Different Surface Temperatures (1 of 2)  The Spectra of Stars with Different Surface Temperatures (2 of 2) The corresponding spectral types are indicated on the right side of each spectrum. (Note that stars of each spectral type have a range of temperature.) The hydrogen Balmer lines are strongest in stars with surface temperatures of about 10,000 K (called A-type stars). Cooler stars (G- and K-type stars) exhibit numerous atomic lines caused by various elements, indicating temperatures from 4000 to 6000 K. Several of the broad, dark bands in the spectrum of the coolest stars (M-type stars) are caused by titanium oxide (TiO) molecules, which can exist only if the temperature is below about 3700 K. Recall from Section 4-5 that the Roman numeral I after a chemical symbol means that the absorption line is caused by a neutral atom; a numeral II means that the absorption is caused by atoms that have each lost one electron.  The Spectral Sequence Spectral Color Temperature (K) Spectral lines Examples class O Blue-violet 50,000–30,000 Ionized atoms, especially Naos ( ζ Puppis), helium Mintaka ( δ Orionis) B Blue-white 30,000–11,000 Neutral helium, some Spica ( α Virginis), hydrogen Rigel ( β Orionis) A White 11,000–7500 Strong hydrogen, some Sirius ( α Canis Majoris), ionized metals Vega (α Lyrae) F Yellow-white 7500–5900 Hydrogen and ionized Canopus (α Carinae), metals, such as calcium Procyon (α Canis Minoris) and iron G Yellow 5900–5200 Both neutral and ionized Sun, Capella (α Aurigae)s metals, especially ionized calcium K Orange 5200–3900 Neutral metals Arcturus (α Boötis), Aldebaran (α Tauri) M Red-orange 3900–2500 Strong titanium oxide and Antares (α Scorpii), some neutral calcium Betelgeuse (α Orionis) Classifying the Spectra of Stars (1 of 2)  Classifying the Spectra of Stars (2 of 2) The modern classification scheme for stars, based on their spectra, was developed at the Harvard College Observatory in the late nineteenth century. Female astronomers, initially led by a) Edward C. Pickering (standing, with observatory computers), then by b) Williamina Fleming, first row center, on a shipboard outing with her observatory computers, and then by c) Annie Jump Cannon (middle row, second from the left), analyzed hundreds of thousands of spectra. Other computers pictured include Margaret Harwood, Cecilia Payne, Arville D. Walker, Edith F. Gill, Lillian L. Hodgdon, Evelyn F. Leland, Ida E. Woods, Mabel A. Gill, Florence Cushman, Agnes M. Hoovens, Mary B. Howe, Harvia H. Wilson, Margaret Walton Mayall, and Antonia C. Maury. Social conventions of the time prevented most female astronomers from using research telescopes or receiving salaries comparable to those of men. A Hertzsprung–Russell Diagram (1 of 3)  A Hertzsprung–Russell Diagram (2 of 3) On an H-R diagram, the luminosities of stars are plotted against their spectral types. Each dot on this graph represents a star whose luminosity and spectral type have been determined. Some well-known stars are identified.  A Hertzsprung–Russell Diagram (3 of 3) The data points are grouped in just a few regions of the diagram, revealing that luminosity and spectral type are correlated: Main-sequence stars fall along the red curve, giants are to the right, supergiants are on the top, and white dwarfs are well below the main sequence. The absolute magnitudes and surface temperatures are listed at the right and top of the graph, respectively. These are sometimes used on H-R diagrams instead of luminosities and spectral types. The Types of Stars and Their Sizes (1 of 3)  The Types of Stars and Their Sizes (2 of 3) On this H-R diagram, stellar luminosities are plotted against the surface temperatures of stars. The dashed diagonal lines indicate stellar radii. For stars of the same radius, hotter stars (corresponding to moving from right to left on the H-R diagram) glow more intensely and are more luminous (corresponding to moving upward on the diagram) than cooler stars.  The Types of Stars and Their Sizes (3 of 3) While individual stars are not plotted, we show the regions of the diagram in which main-sequence, giant, supergiant, and white dwarf stars are found. Note that the Sun is intermediate in luminosity, surface temperature, and radius; it is very much a middle-of- the-road star. Stellar Size and Spectra (1 of 2)  Stellar Size and Spectra (2 of 2) These spectra are from two stars of the same spectral type (B8) and, hence, the same surface temperature (13,400 K) but different radii and luminosities: a) the B8 supergiant Rigel (luminosity 58,000 Lʘ) in Orion and b) the B8 main-sequence star Algol (luminosity 100 Lʘ) in Perseus. Luminosity Classes (1 of 2)  Luminosity Classes (2 of 2) Dividing the H-R diagram into regions, called luminosity classes, permits finer distinctions between giants and supergiants. – Luminosity classes Ia and Ib encompass the supergiants. – Luminosity classes II, III, and IV indicate giants of different brightness. – Luminosity class V indicates main-sequence stars. Because they do not create energy by fusion, like the other stars we have discussed so far, white dwarfs do not have their own luminosity class.  Spectrographic Parallax (1 of 2) 1. Astronomers observe a distant star’s apparent magnitude and spectrum. 2. From its spectrum, they determine what spectral class the star belongs to (or, equivalently, its surface temperature).  Spectrographic Parallax (2 of 2) 3. The spectrum also reveals the star’s luminosity class, that is, whether it is a supergiant, giant, or main- sequence star. Combining the temperature and the luminosity class determines the star’s location on the H-R diagram (see Figure 12-10 ). From this position, the star’s approximate absolute magnitude can be read off the diagram. 4. Using the apparent and absolute magnitudes in the distance-magnitude relationship (see An Astronomer’s Toolbox 12-3: The Distance-Magnitude Relationship), the star’s distance can then be calculated.  Stellar Mass The mass of each star determines how strongly it can compress and heat its interior and thereby create light and other electromagnetic radiation by thermonuclear fusion. The problem with finding stellar masses is that it cannot be done directly by examining isolated stars. The mass of a star can be determined only by its gravitational effects on other bodies, using Newton’s law of gravity. Fortunately for astronomers, more than half of the stars near our solar system are members of star systems in which two stars orbit each other.  Binary Stars (1 of 2) A pair of stars located at nearly the same position in the night sky is called a double star. Some double stars are not physically close together and do not orbit each other. These optical doubles just happen to lie in the same direction, as seen from Earth. Other double stars are true binary stars—pairs in which two stars orbit a common center of mass.  Binary Stars (2 of 2) In the case of visual binaries, both stars can be seen, using a telescope if necessary (Figure 12-11). Astronomers can plot the orbits of the stars in a visual binary. 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 the binary’s light curve. A Binary Star System (1 of 3)  A Binary Star System (2 of 3) About one-third of the objects we see as “stars” in our region of the Milky Way Galaxy are actually double stars. Mizar in Ursa Major is a binary system with stars separated by only about 0.01 arcsec. The images and plots show the relative positions of the two stars over nearly half of their orbital period.  A Binary Star System (3 of 3) The orbital motion of the two binary stars around each other is evident. Either star can be considered fixed in making such plots. (Technically, this pair of stars is Mizar A and its dimmer companion. These two are bound to another binary pair, Mizar B and its dimmer companion.) Center of Mass of a Binary Star System (1 of 2) Center of Mass of a Binary Star System (2 of 2) a) Two stars move in elliptical orbits around a common center of mass. Although the orbits cross each other, the two stars are always on opposite sides of the center of mass and thus never collide. b) A seesaw balances if the center of mass of the two children is at the fulcrum. When balanced, the heavier child is always closer to the fulcrum, just as the more massive star is closer to the center of mass of a binary star system. Representative Light Curves of Eclipsing Binaries (1 of 2)  Representative Light Curves of Eclipsing Binaries (2 of 2) The shape of the light curve (blue) reveals that the pairs of stars have orbits in planes nearly edge-on to our line of sight. It also provides details about the two stars that make up an eclipsing binary. Illustrated here are a) a partial eclipse and b) a total eclipse. c) The binary star NN Serpens, indicated by the arrow, undergoes a total eclipse. The telescope was moved during the exposure so that the sky drifted slowly from left to right. During the 10.5-minute eclipse, the dimmer but larger star in the binary system (an M6 V star) passed in front of the more luminous but smaller star (a white dwarf). The binary became so dim that it almost disappeared. The Stellar Masses of the Binary Star System Sirius A and Sirius B (1 of 2)  The Stellar Masses of the Binary Star System Sirius A and Sirius B (2 of 2) a) The bright star Sirius (Sirius A) in Canis Major has long been known to be part of a binary system. The system is only 8.5 ly from our solar system. b) After years of careful measurement, plotted in this diagram, the orbits of these two stars have been determined with extreme precision, thereby enabling astronomers to calculate their masses to high precision: Sirius A: 2.063 +/- 0.023 Mʘ and Sirius B: 1.018 +/- 0.011 Mʘ The Mass-Luminosity Relation (1 of 3)  The Mass-Luminosity Relation (2 of 3) a) For main-sequence stars, mass and luminosity are directly correlated—the more massive a star, the more luminous it is. A main-sequence star of mass 10 Mʘ has roughly 3000 times the Sun’s luminosity (3000 Lʘ); one with 0.1 Mʘ has a luminosity of only about 0.001 Lʘ. To fit the whole sequence on one page, the luminosities and masses are plotted using logarithm scales.  The Mass-Luminosity Relation (3 of 3) b) Equivalently, 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 (Mʘ). 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. Spectral-Line Motion in Binary Star Systems (1 of 3)  Spectral-Line Motion in Binary Star Systems (2 of 3) The diagrams at the top indicates the positions and motions of the stars, labeled A and B, relative to Earth. Below each diagram is the spectrum we would observe for these two stars at each stage. The changes in colors (wavelengths) of the spectral lines are due to changes in the Doppler shifts of the stars, as seen from Earth.  Spectral-Line Motion in Binary Star Systems (3 of 3) The graph displays the radial-velocity curves of the binary HD 171978. (The HD means that this is a star from the Henry Draper Catalogue of stars.) The entire binary is moving away from us at 12 km/s, which is why the pattern of radial velocity curves is displaced upward from the zero-velocity line. A Double-Line Spectroscopic Binary (1 of 2)  A Double-Line Spectroscopic Binary (2 of 2) The spectrum of the double-line spectroscopic binary κ (kappa) Arietis has spectral lines that shift back and forth as the two stars revolve around each other. a) The stars are moving parallel to the line of sight, with one star approaching Earth, the other star receding, as in Stage 1 or 3 of Figure 12-16. These motions produce two sets of shifted spectral lines. b) Both stars are moving perpendicular to our line of sight, as in Stage 2 or 4 of Figure 12-16. As a result, the spectral lines of the two stars have merged. Summary of Key Ideas  Star Characteristics Stars differ in size, luminosity, temperature, color, mass, and chemical composition—facts that help astronomers understand stellar structure and evolution.  Magnitude Scales (1 of 2) 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 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.  Magnitude Scales (2 of 2) 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 from Earth. The luminosity of a star is the amount of energy it emits each second.  The Temperatures of Stars Stellar temperatures can be determined from star 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.  Types of Stars (1 of 2) 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.  Types of Stars (2 of 2) 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, a method called spectroscopic parallax.  Stellar Masses (1 of 2) Binary stars are fairly 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. 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.  Stellar Masses (2 of 2) 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 the binary’s light curve.  Key Terms (1 of 3) 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  Key Terms (2 of 3) light curve luminosity luminosity class main sequence main-sequence star mass-luminosity relation OBAFGKM sequence optical double photometry radial-velocity curve  Key Terms (3 of 3) red giant spectral types spectroscopic binary spectroscopic parallax stellar evolution stellar parallax stellar spectroscopy supergiant visual binary white dwarf