Week #8 Notes

1. Week #8 Notes Stars: Distant Suns

2. Colors, Temperatures, andSpectra of Stars • To understand the temperature of the poker or of a hot gas, we measure its spectrum (see figure). • A dense, opaque gas or a solid gives off a continuous spectrum—that is, light changing smoothly in intensity (brightness) from one color to the next. • When you heat an iron poker in a fire, it begins to glow and then becomes red hot. • If we could make it hotter still, it would become white hot, and eventually bluish-white.

3. Colors, Temperatures, andSpectra of Stars • Black Body is a perfect emitter: Its spectrum depends only on its temperature, not on chemical composition or other factors. • We can approximate the spectrum of the visible radiation from the outer layer of a star as a black-body curve. • The black-body curve is also called the Planck curve, in honor of the physicist Max Planck.

4. Colors, Temperatures, andSpectra of Stars • A different black-body curve corresponds to each temperature (see figure). • Note that as the temperature increases, the gas gives off more energy at every wavelength. • Indeed, per unit of surface area, a hot black body emits much more energy per second than a cold one. • Moreover, the wavelength at which most energy is given off is farther and farther toward the blue as the temperature increases. • The wavelength of this peak energy is shown with a dashed line. • At temperatures of 4000 K, 5000 K, 6000 K, and 7000 K, the peak of the black-body curve is at wavelengths of 7200 Å (red), 5800 Å (yellow), 4800 Å (blue), and 4100 Å (violet), respectively. • Thus, the hottest stars look blue and the coolest ones are red.

5. Colors, Temperatures, andSpectra of Stars • Those of intermediate temperature (like the Sun) appear white, despite having spectra that peak around yellow or green wavelengths, because of the physiological response of our eyes. • By simply measuring the wavelength of the peak brightness of a star’s spectrum, astronomers can take the star’s temperature (though not with great accuracy.)

6. How Do We Classify Stars? • All the spectral lines of normal stars are absorption lines, also called dark lines. • The absorption lines cause a star’s spectrum to deviate from that of a black body, but not by much. • Studying the absorption lines has been especially fruitful in understanding the stars and their composition. • We can duplicate on Earth many of the contributors to the spectra of the stars. • Since hydrogen has only one electron, hydrogen’s spectrum (Chapter 2) is particularly simple (see figure). • Atoms with more electrons have more possible energy levels, resulting in more choices for jumps between energy levels. • Consequently, elements other than hydrogen have more complicated sets of spectral lines.

7. How Do We Classify Stars? • When we look at a variety of stars, we see many different sets of spectral lines, usually from many elements mixed together in the star’s outer layers. • Hydrogen is usually prominent, though often iron, magnesium, sodium, or calcium lines are also present. • The different elements can be distinguished by looking for their distinct patterns of spectral lines.

8. How Do We Classify Stars? • Early in the 20th century, Annie Jump Cannon at the Harvard Observatory classified hundreds of thousands of stars by their visible-light spectra (see figure). • She first classified them by the strength of their hydrogen lines, defining stars with the strongest lines as “spectral type A,” stars of slightly weaker hydrogen lines as “spectral type B,” and so on. (Many of the letters wound up not being used.)

9. How Do We Classify Stars? • It was soon realized that hydrogen lines were strongest at some particular temperature, and were weaker at hotter temperatures (because the electrons escaped completely from the atom) or at cooler temperatures (because the electrons were only in the lowest possible energy levels, which do not allow the visible-light hydrogen lines to form). • Rearranging the spectral types in order of temperature—from hottest to coolest—gave O B A F G K M. • Recently, even cooler objects—stars and brown dwarfs—have been found, and are designated L-type and (still more recently) T-type. Generations of astronomy students have memorized the order using the mnemonic “Oh, be afine girl [or guy], kiss me.” • Think of your own mnemonic for O B A F G K M L T.

10. How Do We Classify Stars? • Looking at a set of stellar spectra in order (see figure) shows how the hydrogen lines are strongest at spectral type A, which corresponds to a surface temperature of roughly 10,000 K.

11. How Do We Classify Stars? • A pair of spectral lines from calcium becomes strong in spectral type G (a type that includes the Sun), at about 6000 K (see figure). • In very cool stars, those of spectral type M, the temperatures are so low (only 3000 K) that molecules can survive, and we see complicated sets of spectral lines from them. • At the other extreme, the hottest stars, of spectral type O, can reach 50,000 K. • Some stars of type O have shells of hot gas around them and give off emission lines, though stars generally show only absorption lines in their spectra.

12. How Do We Classify Stars? • Astronomers subdivide each spectral type into ten subtypes ranging from hottest (0) to coolest (9); thus, for example, we have A0 through A9, and then F0 through F9. • One of the first things most astronomers do when studying a star is to determine its spectral type and thus its surface temperature. • The Sun is a type G2 star, corresponding to a temperature of 5800 K. • We have known that stars are made mainly of hydrogen and helium only since the 1920s.

13. How Distant Are the Stars? • We often unconsciously judge how far away an object is by assessing its apparent size compared with the sizes of other objects. • But the stars are so far away that they appear as points, so we cannot judge their size. • Only for the nearest stars can we reliably measure their distance fairly directly even with our best methods.

14. How Distant Are the Stars? • The distances of nearby stars can be determined by triangulation (also known as “trigonometric parallax”)—a sort of binocular vision obtained by taking advantage of our location on a moving platform (the Earth). • The basic idea is that the position of a nearby object shifts relative to distant objects when viewed from different lines of sight (see figure). • For example, if you put a finger in front of your eyes, and close one eye, the finger will appear to be projected against a particular background object. • If you close this eye and open the other one, the position of the finger will shift to a different background object. • The amount of shift is smaller if the finger is farther away.

15. How Distant Are the Stars? • Here’s how we apply this method to nearby stars. • At six-month intervals, the Earth carries us entirely across its orbit, halfway around (see figure, top). • Since the average radius of the Earth’s orbit is 1 astronomical unit (A.U.), we move by 2 A.U. This distance is enough to give us a somewhat different perspective on the nearest stars. • These stars appear to shift very slightly against the background of more distant stars. • Clearly, the more distant the star, the smaller is its angular shift (see figure, bottom). • The nearest star—known as Proxima Centauri—appears to shift by only the diameter of a dime at a distance of 2.4 km! • It turns out to be about 4.2 light-years away. (It is in the southern constellation of Centaurus, and is not visible from most of the United States.)

16. How Distant Are the Stars? • By calculating the length of the long side of a giant triangle—by “triangulating”—we can measure distances in this way out to a few hundred light-years. • But there are only a few thousand stars that are so close to us, and at the farthest distances the results are not very accurate. • The European Space Agency lofted a satellite, Hipparcos, in 1989 to measure the positions of stars. • Measuring the positions and motions of stars is known as astrometry. • Based on its data, in 1997 the scientists involved released the Hipparcos catalogue, containing distances for 118,000 stars, relatively accurate to about 300 light-years away. • A secondary list, the Tycho-2 catalogue, contains less-accurate distances for a million stars but provides accurate “proper motions” (motion across the sky, which we will discuss in Section 11.5) for a total of two and a half million stars.

17. How Distant Are the Stars? • Our Milky Way Galaxy is perhaps 100,000 light-years across, so even the 600 lightyears (diameter) spanned by the Hipparcos catalogue takes up less than 1 per cent of the diameter of our Galaxy. • A successor European Space Agency spacecraft (Gaia) is still on the books for launch in 2011, or beyond. • Also, NASA’s Space Interferometry Mission (recently renamed SIM PlanetQuest), is also planned for a 2011 launch; it will provide measurements of the positions of stars in our Galaxy with unprecedented accuracy, thereby leading to much improved distances.

18. How Powerful Are the Stars? • Automobile headlights appear faint when they are far away but can almost blind us when they are up close. • A star’s intrinsic brightness is its luminosity, or “power.” • If we use units that show the amount of energy a star gives off in a given time, the Sun’s luminosity, for example, is 4 x 1026 joules/second, where a joule (symbol J) is a unit of energy. (Sometimes you will see energy given in ergs, a smaller unit of energy. One joule is 10 million ergs.) • We have previously described (in Chapter 4) how we give stars’ apparent brightnesses in “apparent magnitude.” • To tell how inherently bright stars are, astronomers often use a modification of the magnitude scale known as absolute magnitude.

19. How Powerful Are the Stars? • To do so, they have set a specific distance at which to compare stars. • Basically, if something is intrinsically fainter, it has a higher absolute magnitude. • You can determine how far away a star is by comparing how bright it looks with its intrinsic brightness (its luminosity, whether measured in joules/second or as absolute magnitude). • The method works because we understand how a star’s energy spreads out with distance (see figure).

20. How Powerful Are the Stars? • The energy received from a star changes with the square of the distance: the energy decreases as the distance increases. • Since one value goes up as the other goes down, it is an inverse relationship. • We call it the inverse-square law. • Using this law, there is a simple way to express the luminosity of a star in terms of its apparent brightness and distance.

21. Temperature-Luminosity Diagrams • If you plot a graph that has the surface temperature of stars on the horizontal axis (x-axis) and the luminosity (intrinsic brightness) of the stars on the vertical axis (y-axis), the result is called a temperature-luminosity diagram. • The luminosity (vertical axis) can also be expressed in absolute magnitudes, so the term “temperature-magnitude diagram”. • Sometimes the horizontal axis is labeled with spectral type, since temperature is often measured from spectral type or from a star’s color (Section 11.1).

22. Temperature-Luminosity Diagrams • If we plot such a diagram for the nearest stars (see figure), we find that most of them fall on a narrow band that extends downward (fainter) from the Sun. • If we plot such a diagram for the brightest stars we see in the sky, we find that the stars are more scattered, but that all are intrinsically brighter than the Sun.

23. Temperature-Luminosity Diagrams • The idea of such plots came to two astronomers in the early years of the 20th century. • Henry Norris Russell (see figure, top), at Princeton University in the United States, plotted the absolute magnitudes (equivalent to luminosities) as his measure of brightness. • Ejnar Hertzsprung (see figure, bottom), in Denmark, plotted apparent magnitudes but did them for a group of stars that were all at the same distance. • He could do this by considering a cluster of stars (Section 11.8), since all the stars in the cluster are essentially the same distance away from us. • The two methods came to the same thing, in that the magnitudes found for different stars could be directly compared. Temperature-luminosity (temperature-magnitude) diagrams are often known as “Hertzsprung–Russell diagrams” or as “H–R diagrams.”

24. Temperature-Luminosity Diagrams • The position of a star on the main sequence turns out to be determined by its mass: Massive stars are hotter and more powerful than low-mass stars. • The position of a star does not change much while it is on the main sequence: The Sun stays at more or less the same position on the main sequence for about 10 billion years. • Stars on the main sequence are called dwarfs, so the Sun is a dwarf. • When we graph quite a lot of stars, or put together both nearby and farther stars (see figure), we can see clearly that most stars fall in a narrow band across the temperature-luminosity diagram. • This band is called the main sequence. • Normal stars in the longest-lasting phase of their lifetime are on the main sequence.

25. Temperature-Luminosity Diagrams • A few stars are more luminous (intrinsically brighter) than main-sequence stars of the same surface temperature. • Since the same surface area of gas at the same temperature gives off the same amount of energy per second, these stars must be bigger than the main-sequence stars. • They are thus called giants or even supergiants. • The reddish star Betelgeuse in the shoulder of the constellation Orion is a supergiant.

26. Temperature-Luminosity Diagrams • A few stars are intrinsically fainter than dwarfs (main-sequence stars) of the same color. • These less luminous stars are called white dwarfs. • Do not confuse white dwarfs with normal dwarfs (main-sequence stars); white dwarfs are smaller than normal dwarfs. • The Sun is 1.4 million kilometers across, while the white dwarf Sirius B (a companion of the bright star Sirius) is only about 10 thousand kilometers across, roughly the size of the Earth.

27. Proper Motions of Stars • The stars are so far away that they hardly move across the sky relative to each other. • Don’t confuse this relative motion of stars with the nightly motion of stars across the sky, which is merely a reflection of Earth’s rotation about its axis, or with the seasonal changes of constellations, which is a reflection of Earth’s orbit around the Sun. • Note that the proper motion is an angular movement of stars across the sky, relative to each other; the units are typically seconds of arc per century.

28. Proper Motions of Stars • Only for the nearest stars can we easily detect any such relative motion among the stars, which is called proper motion(see figure). • However, for the most precise work astronomers have to take the effect of the proper motions (over decades) into account. • The Hipparcos satellite has improved our measurements of many stars’ proper motions, and the future Space Interferometry Mission (SIM PlanetQuest) will provide enormous amounts of additional data.

29. Radial Velocities of Stars • Astronomers can actually measure motions toward and away from us (that is, along our line of sight) much better than they can measure motions from side to side, in the plane of the sky (perpendicular to our line of sight). • Recall that a motion toward or away from us on a line joining us and a star (a radius) is called a radial velocity. • A radial velocity shows up as a Doppler shift, a change of the spectrum so that anything that originally appeared at a given wavelength now appears at another wavelength.

30. Radial Velocities of Stars • Doppler shifts in sound are more familiar to us than Doppler shifts in light. • You can easily hear the pitch of a car’s engine drop as the car passes us. • A similar effect takes place with light when we observe light that was emitted by an object that is moving toward or away from us. • The effect, though, is not obvious to the eye; sensitive devices are necessary to detect the Doppler shift in light.

31. Radial Velocities of Stars • For the case of the moving emitter, observers who are being approached by the emitting source see the three peaks coming past them bunched together. • They pass at shorter intervals of time, as though the wavelengths were shorter. • This situation corresponds to a color for each wavelength farther to the blue than it started out, so is called a blueshift. • Observers from whom the emitter is receding see the three peaks at increased intervals of time, as though the wavelengths were longer. • This situation corresponds to a color for each wavelength farther to the red than it started out, a redshift.

32. Radial Velocities of Stars • By contrast, for the stationary emitter, all the peaks are centered on the same point. • No redshifts or blueshifts arise. • So whenever an object is moving away from us, its spectrum is shifted slightly to longer wavelengths. • We say that the object’s light is redshifted. • When an object is moving toward us, its spectrum is blueshifted, that is, shifted toward shorter wavelengths.

33. Radial Velocities of Stars • The fraction of its wavelength by which light is redshifted or blueshifted is the same as the fraction of the speed of light that the object is moving. (That is, the wavelength shift is proportional to the speed of the object.) • So astronomers can measure an object’s radial velocity by measuring the wavelength of a spectral line and comparing the wavelength to a similar spectral line measured from a stationary source on Earth (see figure).

34. Radial Velocities of Stars • Stars in our Galaxy have only small Doppler shifts, which shows that they are travelling at less than 1 per cent of the speed of light. • Though they may be redshifted or blueshifted, the shifts are not enough to change the color that we see when we look at these stars.

35. “Social Stars”: Binaries • Though the Sun is an isolated star in space, most stars are members of pairs or groups. • If our planet were part of such a system, we might see two or more Suns rising and setting • If our Sun were part of a cluster of stars, the nighttime sky would be ablaze with very bright points of light.

36. Pairs of Stars and Their Uses • Sometimes, a star that looks double appears so merely because two unconnected stars happen to appear in essentially the same direction. • They are thus examples of optical doubles, chance apparent associations. • For example, if you look up at the Big Dipper, you might be able to see, even with your naked eye, that the middle star in the handle (Mizar) has a fainter companion (Alcor). • Native Americans called these stars a horse and rider. • However, over 50 per cent of the apparently single “stars” you see in the sky are actually multiple systems bound by gravity and orbiting each other. (More precisely, the stars orbit their mutual, or common, center of mass.) • Astronomers take advantage of such binary stars (or simply “binaries”) to find out how much mass stars contain.

37. Visual Binaries • When you look at Mizar through a telescope, even after separating it from Alcor you can see that it is split in two. • In fact, Mizar was the first double star to have been discovered telescopically (in 1650). • These two stars are revolving around each other, and are thus known as a visual binary. • We see visual binaries best when the stars are relatively far away from each other in their mutual orbits (see figure).

38. 11.6a(ii) Spectroscopic Binaries • The two components of Mizar are known as Mizar A and Mizar B. • If we look at the spectrum of either one (see figure, top), we can see that over a period of days, the spectral lines seem to split and come together again. • The spectrum shows that two stars are actually present in Mizar A, and another two are present in Mizar B. • They are spectroscopic binaries, since they are distinguished by their spectra.

39. Eclipsing Binaries • Yet another type of binary star is detectable when the light from a star periodically dims because one of the components passes in front of (eclipses) the other (see figure). • From Earth, we graph the “light curves” of these eclipsing binaries by plotting their brightnesses over time.

40. Eclipsing Binaries • Eclipsing binaries are detected by us only because they happen to be aligned so that one star passes between the Earth and the other star. • Thus all binaries would be eclipsing if we could see them at the proper angle. (At least a few planets around distant stars have been detected in a similar fashion, by a dimming of the total light when it passes in front of, or transits, its parent star.) • Since one star can eclipse another only when we are in the plane of its orbit, we know that we are seeing the orbit edge-on and can calculate the masses of the component stars. • We can accurately measure stellar masses only for eclipsing binaries.

41. Eclipsing Binaries • The same binary system might be seen as different types depending on the angle at which we happen to view the system (see figure).

42. Astrometric Binaries • One more type of double star can be detected when we observe a wobble in the path of a star as its proper motion, its motion with respect to other stars in our Galaxy, takes it slowly across the sky (see figures). • The laws of physics hold that a moving mass must move in a straight line unless affected by a force. • The wobble away from a straight line tells us that the visible star must be orbiting an invisible object, pulling the visible star from side to side. • Since measurement of the positions and motions of stars is known as astrometry, these stars are called astrometric binaries.

43. How Do We Weigh Stars? • A primary use of binary stars is the measurement of stellar masses (informally, “weighing” stars). • We can sometimes determine enough about the stars’ orbits around each other that we can calculate how much mass the stars must have to stay in those orbits. • It turns out that the mass of a star is its single most important characteristic: Essentially everything else about its properties and evolution depends on mass. • In particular, massive main-sequence stars are far more luminous and have much shorter lives than low-mass main-sequence stars. • Though massive stars start with more fuel, they consume it at a huge rate.

44. Stars That Don’t Shine Steadily • Some stars vary in brightness over hours, days, or months. • Eclipsing binaries are one example of such variable stars, but other types of variable stars are actually individually changing in brightness. • Many professional and amateur astronomers follow the “light curves” of such stars, the graphs of how their brightness changes over time.

45. Stars That Don’t Shine Steadily • A very common type of variable star changes slowly in brightness with a period of months or up to a couple of years. • The first of these long-period variables to be discovered was the star Mira in the constellation Cetus, the Whale (see figure, left). • At its maximum brightness, it is 3rd magnitude, quite noticeable to the naked eye. • At its minimum brightness, it is far below naked-eye visibility (see figure, right). • Such stars are giants whose outer layers actually change in size and temperature.

46. Stars That Don’t Shine Steadily • A particularly important type of variable star for astronomers is the Cepheid variable, of which the star d (the Greek letter “delta”) Cephei is a prime example (see figures). • A strict relation exists linking the period over which the star varies with the star’s average luminosity (average intrinsic brightness).

47. Stars That Don’t Shine Steadily • Stars of a related type, RR Lyrae variables, have shorter periods—only several hours long—than regular Cepheids. • RR Lyrae variables are often (but not exclusively) found in clusters of stars, groupings of stars. • Since all RR Lyrae stars have the same average luminosity (average intrinsic brightness), observing an RR Lyrae star and comparing its average apparent brightness with its average luminosity enables us to tell how far away the cluster is.

48. Clusters of Stars • Clusters, or physical groups of stars in the Milky Way Galaxy, come in two basic varieties. • Clusters in other galaxies have similar properties, though there may be a few differences in detail (e.g., some globular clusters in other galaxies may be young, unlike the case in our Galaxy).

49. 1Open and Globular Star Clusters • The face of Taurus, the Bull, is outlined by a “V” of stars, which are close together out in space. • On Taurus’s back rides another group of stars, the Pleiades (pronounced Pleeadeez). • Both are examples of open clusters, groupings of dozens or a few hundred stars. • We can often see 6 of the Pleiades stars with the naked eye, but binoculars reveal dozens more and telescopes show the rest.

50. 1Open and Globular Star Clusters • Open clusters (see figures) are irregular in shape. • About 1000 open clusters are known in our Galaxy. • They are found near the band of light called the Milky Way (see Chapter 15), which means that they are in the plane of our Galaxy. • Specifically, they are generally in or near our Galaxy’s spiral arms. (They are often known as “galactic clusters”.) • They are only loosely bound by gravity, gradually dissipating (“evaporating”) away as individual stars escape.