HW10 - MasteringAstronomy 4/5/10 11:32 AM \liumgv llu.»...

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Unformatted text preview: MasteringAstronomy 4/5/10 11:32 AM \liumgv llu.» \nxignirrt'nt Print Verslo HW10 (questions from chapt 17 and 20 email me questions) Due: 11:59pm on Thursday, April 22, 2010 Note: You will receive no credit for late submissions. To learn more, read your instructors Gradan Policy Ranking Task: H-R Diagram, Luminosity, and Temperature Description: A multi-part activity requiring reasoning about the surface temperature and luminosity of stars as indicated on the H-R diagram. Part A Consider the four stars shown following. Rank the stars based on their surface temperature from highest to lowest. Hint A.l How is the color of light related to its wavelength? Which of the following lists the visible colors in correct order from shortest wavelength to longest wavelength? ANSWER: ' - actually peaks in the green. You should then be able to complete the ranking task in Part A. Hint A.2 How does the wavelength of light depend on an object’s temperature? According to the laws of thermal radiation, hotter objects have spectra that peak at ANSWER: E ashorterwavelength ’lon er \vavelen th The object’s color generally looks like the color of light at the peak wavolength. Now, remember that shorter wavelength means bluer light, and you should be able to complete the ranking task in Part A. Hint At3 ‘ The—Colorwof the Sun The Sun appears yellow or white to the eye, but its spectrum actually peaks in the middle of the Visible region, which corresponds to yellow or green in color. Note that this means the Sun‘s spectrum peaks at a wavelength shorter than that of a blue star. but longer than that of an orange or red star. Notice that temperature is related to color, and follows the order of the colors in the rainbow: Blue (or violet) stars are the hottest, while red stars are the coolest. In the parts that follow. the H-R diagrams show the correlation between color and temperature on the horizontal axis. Five stars are shown on the following H~R diagrams. Rank the stars based on their surf ace temperature from highest to lowest. If two (or more) stars have the same surface temperature, drag one star on top of the other(s). Hint 3.1 How does the H-R diagram show surface temperature? On the H—R diagram, surface temperature increases . pward, so stars low on the luminosity axis have lower surface temperature than stars higher up aright to left, so stars farther to the left along the spectral type axis have higher surface temperature than stars to the right agonally from the lower left to the upper right ANSWER: e, X“ a”; M having the lowest surface temperature. Now. look to see how the surface temperatures of the five stars compare and you will then be able to complete Part B of this ranking task. ANSWER: All five stars appear at the same place along the horizontal axis showing spectral type. Because spectral type is related to surface temperature, all five stars must have the same surface temperature. Now proceed to Part C to determine how these stars vary in luminosity. Part C Five stars are shown on the following H-R diagrams; notice that these are the same five stars shown in Part B, Rank the stars based on their http://session.masteringastronomy.com/myct Page 1 of 17 MasteringAstronomy luminosity from highest to lowest. If two (or more) stars have the same luminosity, drag one star on top of the other(s). luminosity axis represents a change by a factor of 10 from the prior tickmark, so the range of luminosities is quite large. Continue to Parts D Luminosity is shown along the Vertical axis, with stars higher up more luminous than those lower down. Note that each tickmark along the U Part D Five stars are shown on the following H—R diagrams. Rank the stars based on their surface temperature from highest to lowest. If two (or more) stars have the same surface temperature, drag one star on top of the other(s). Hint D.l How does the H-R diagram show surface temperature? On the 1-D? diagram. surface temperature increases ANSWER: E » upward, so stars low on the luminosny axts have lower surface temperature than stars higher up I @right to left, so stars farther to the left along the spectral type axis have higher surface temperature than stars to the right « diagonally from the lOWer left to the upper right Spectral type is related to surface temperature, with stars of spectral type 0 haying the highest surface temperature and stars of spectral type 3% M having the lowest surface temperature. Now, look to see how the surface temperatures of the five stars compare and you will then be able to complete Part B of this ranking task. ANSWER: i i t r’ l ' Spectral type is related to surface temperature, with stars of spectral type 0 having the highest surface temperature and stars of spectral type M having the lowest surface temperature. In other words, spectral type increases to the left on the H—R diagram. Now proceed to Part E to determine how these stars compare in luminosity. Part E Five stars are shown on the following H-R diagrams. Rank the stars based on their luminosity from highest to lowest; notice that these are the same five stars shown in Part D. If two (or more) stars have the same luminosity, drag one star on top of the other(s). ANSWER All five stars have the same luminosity because they are all at the same height along the vertical (luminosity) axis. Continue to Parts F and G T for more practice in reading surface temperature and luminosity on the HR diagram. Five stars are shown on the following H—R diagrams. Rani: the stars based on their surface temperature from highest to lowest. If two (or more) stars have the same surface temperature, drag one star on top of the other(s). Hint F.l How does the H-R diagram show surface temperature? On the H—R diagram, surface temperature increases ANSWER: upward, so stars low on the luminosity axis have lower surface temperature than stars higher up 3 § @right to left, so stars farther to the left along the spectral type axis have higher surface temperature than stars to the right I ‘diagonally from the IOWer left to the upper right httpzl/sessIon.masterlngastronomy.com/myct 4/5/10 11:33 AM Page 2 of 17 MasteringAstronomy 4/5/10 11:33 AM l View Spectral type is related to surface temperature, with stars of spectral type 0 having the highest surface temperature and stars of spectral typeM having the lowest surface temperatur In other words, spectral type increases to the left on the H-R diagram. Part C Five stars are shown on the following H-R diagrams; notice that these are the same five stars shown in Part F. Rank the stars based on their luminosity from highest to lowest. If two (or more) stars have the same luminosity, drag one star on top of the other(s). ANSWER: s always, the HR diagram shows surface temperature along the horizontal axis and luminosity along the vertical axis. Ranking Task: Luminosity, Distance, and the Apparent Brightness of Stars ~ ‘l Description: A multi-part ranking task exploring the relationship among luminosity, apparent brightness, and distance. Part A —l Listed following are several fictitious stars with their luminosities given in terms of the Sun’s luminosity ( L5,“) and their distances from Earth git’en in light—years (1y). Rank the stars based on how bright each would appear in the sky as seen from Earth, from brightest to dimmest. If two (or more) stars have the same brightness in the sky, show this equality by dragging one star on top of the other(s). Hint A.1 What is luminosity? ANSWER: the total amount of light that it radiates into space . 5 7 how bright it is in the night sky The luminosity of a star tells us how lar e the star is in size (radius) l é; The star's brightness in our sky depends on both its luminosity and its distance from us, in accord with the inverse square law for light. You > can use this fact to determine all the correct rankings for Part A. If you need to review the inverse square law for light, consult your textbook F‘g or open the third hint. as Hint A.2 How does a star‘s brightness in our sky depend on its luminosity? Suppose Star X is twice as luminous as Star Y, and both stars are located the same distance from Earth. Then in our night sky, Star X will appear ANSWER: Ihalf as bright as Star Y @twice as bright as Star Y i one-fourth as bright as Star Y r 'four times as bright as Star Y all' b‘ ht Sta Y For a star at a given distance, brightness in our sky is directly proportional to luminosity. Now use this fact along with the inverse square law 8 for light to complete the ranking task. If you need to review the inverse square law for light, consult your textbook or open the third hint. Hint A.3 How does a star's brightness in our sky depend on its distance? Suppose Star X and Star Y have the same luminosity, and Star X is located twice as far from Earth. Then in our night sky, Star X will appear half as bright as StarY ', itwice as bright as Star Y @one-fourth as bright as Star Y ’ Ifour times as bright as Star Y equally as bright as Star Y ANSWER: : a”; g; Brightness in the sky depends on distance in accord with the inverse square law for light: Increasing distance by some factor causes the ~ apparent brightness to decrease (the “inverse” part of the inverse square law) by the square of that factor. For example, doubling distance . decreases the brightness by a factor of 22 = 4, tripling the distance decreases the brightness by a factor of 32 = 9, and so on. This fact is the 1 key to completing the ranking task. Hint A.4 If you are still stuck, open this hint for a strategy to find the answer. The key to completing this ranking task is to compare pairs of stars with the help of the inverse square law for light. 0 Start by comparing Nismo to Shelby: Notice that both have the same luminosity, but Nismo is closer to us. Which one is brighter in our sky? The answer to this question will tell you the ranking order for these two stars. - Next, compare Shelby and Enzo. You will need to use the inverse square law for light to determine which one is brighter, and once you do so you’ll know how to rank these two stars. 0 Then compare Lotus to Enzo, At this point, you should have all the stars ranked except for Ferdinand. - Finally, compare Ferdinand to Shelby, and then you will be done. ANSWER: http://session.masteringastronomy.com/myct Page 3 of 17 MasteringAstronomy ' To be sure you understand the concept, notice the following facts: (1) Nismc is clearly brighter in the sky than Shelby, because it has the same uminosity but is nearer to us. (2) Enzo is twice as luminous and twice as far as Shelby; the inverse square law for light tells us that doubling distance makes an object four times as dim, so Enzo must be dimmer than Shelby. (3) Similarly, because Lotus has twice the luminosity and wice the distance of Enzo, it must be dimmer than Enzo. (4) Ferdinand has four times the luminosity and twice the distance of Shelby, so the nverse square law for light tells us that they are equally bright in our sky. Putting all four facts together leads to the correct answer. Pan B Listed following is the same set of fictitious stars given in Part A. Rank the stars based on how bright each would appear in the sky as seen from Jupiter, from brightest to dimmest. Hint B.l Are the stars closer to Earth or to Jupiter? Compared to their distance from Earth, the stars are _____ Jupiter. closer to E «_»farther from g @about the same distance from ANSWER. Recall that in a 1~to~10—billion scale model, Earth and Jupiter each lie within a few minutes' walk of the grapefruit—size Sun, while even the nearest stars are thousands of kilometers away. As a result, there is no noticeable difference between the way stars will appear in Earth’s sky and the way the same stars will appear in Jupiter‘s sky. ANSWER: I Stars are so far away that any difference in distance to the stars from Earth and Jupiter is negligible. As a result, the answer to this part is the ame as the answer to Part A. Part C The following figure shows how four identical stars appear in the night sky seen from Earth. The shading is used to indicate how bright (white) or dim (dark gray) the star would appear in the sky from Earth. Rank the stars based on their distance from Earth, from farthest to closest. ANSWER: 5 i r r r l i i For stars of the same luminosity. apparent brightness decreases with distance (following the inverse square law for light). Therefore, the star . that appears dimmest must be the most distant and the star that appears brightest must be the nearest. Remember that this is true ONLY if you ;: know that all stars have the same intrinsic luminosity. Because there is no way to know luminosity just by looking at a star in the sky, you ; cannot in general use brightness to say anything about distance. s, , Sorting Task: Patterns among Stars t :Description: A sorting task in which students identify distinguishing characteristics of white dwarfs, main-sequence stars, and giants and supergianls. Part A Listed following is a set of statements describing individual stars or characteristics of stars. Match these to the appropriate object category. Hint A.l What are giant and super-giant stars? Giants and supergiants exceed most other stars in ANSWER: surface temperature only 7 ’luminosity only ‘ ‘radius only @both radius and luminosity ' both surface temperature and luminosity r l i l r r t @ iants and supergiants are found in the upper right portion of the H~R diagram, indicating high luminosity but relatively low surface temperature, which means they must be very large in radius. Hint A.2 What are main-sequence stars? httpzl/session.masteringastronomy.com/myct 4/5/10 11:33 AM Page 4 of 17 MasteringAstronomy ANSWER: l I l i a rare type of extremely massive star l Main~sequence stars are . stars that are in the longest~lasting phase of their lives, in which they fuse hydrogen into i ‘ helium in their cores i ’ stars that have e ’hathted their supplies of energy for fusion i i i gMain-sequence stars therefore represent the vast majority of all stars. Hint A.3 What are white dwarfs? ANSWER: ® dim I . Y i Ivcry luminous : White dtt arfs are small and _. V ,Shon lived ‘ool White dwarfs are dim but hot stellar corpses — essentially the exposed cores of stars that have shed their outer layers — which is why they are found in the lower left of the H—R diagram. i i i i i i i " Be sure that you understand why each of these characteristics goes with either giants/supergiants, main~sequence stars, or white dwarfs. If you tat Visual Activity: Using an H-R Diagram to Explore the Properties of Main-Sequence Stars Description: A multi-part visual activity that uses an interactive H-R diagram to explore the properties of main-sequence stars. Explore the interactive figure before beginning to answer the questions. Click the “show stars” button to see the main sequence and then move the “radius” slider (at bottom) to see the location along the main sequence of a main~sequence star with that particular radius. You can do the same for temperature, luminosity, mass, or lifetime: Clicking one of these properties in the list along the right changes the slider to that property. Note that this interactive figure allows you to vary properties of main-sequence Stars only, not of any other type of star (such as giants or white dwarfs). Part A Compared to a main«sequence star with a short lifetime, a main-sequence star with a long lifetime is Hint A.1 What is the surface temperature of a high-luminosity main-sequence star? A typical surface temperature for a high-luminosity mainvsequence star is less than about 10,000 K I fibetween about 10,000 K and 50,000 K i ‘ greater than about 50,000 K ANSWER: As you can see when you click "show stars," high—luminosity main-sequence stars are in the upper left of the diagram, and the left stde corresponds to surface temperatures ranging from above 10,000 to about 50,000 K. Now, use the interactive figure to determine whether these high-luminosit ' mam»sequence stars have long or sh l f mes. [Hint A.2 What is the mass of a hot main-sequence star? A typical mass for a mainvsequcnce star with high surface temperature is httpzl/session.masteringastronomy.com/myct 4/5/10 11:33 AM Page 5 of 17 MasteringAstronomy 4/5/10 11:33 AM ANSWER: i ’less than about 5 solar masses @between about 5 and 100 solar masses ‘ i greater than about 100 solar masses 5" Notice that surface temperature increases to the left on the diagram, so high-surface-temperature stars are those on the left side. If you use a . more luminous. hotter, larger, and more massive more luminous, hotter, smaller, and less massive less luminous, cooler, larger, and more massive @less luminous, cooler, smaller, and less massive g; Note that there are physical reasons why long-lived stars have these properties: They are less luminous because they burn their fuel at a much lower rate than short-lived stars; they burn it at this lower rate because they are less massive (which means less compression and hence a lower , 1 fusion rate in their cores); and their lower masses lead to their smaller sizes and lowar surface temperatures. Part B Compared to a high—luminosity main—sequence star, stars in the upper right of the H-R diagram are [Hint B.l Which star is hotter? Be sure you have clicked on the "show stars" button and then locate Spica (near the top of the main sequence) and Betelgeuse (near the upper right) in the H-R diagram. True or False? Spica has a higher surface temperature than Betelgeuse. / Be sure to notice that temperature increases to the left on the H—R diagram. % Hint B.2 Which star is larger? Be sure you have clicked on the "show stars" button and then locate Spica (near the top of the main sequence) and Betelgeuse (near the upper right) in the H—R diagram. True or False? Bctelgeuse is larger in radius than Spica. Be sure to notice the diagonal lines showing that radius increases from the lower left to the upper right on the H-R diagram. ANSWER: hotter and larger in radius : @cooler and larger in radius ' ‘ ‘ cooler and smaller in radius . hotter and smaller in radius i 9 Be sure to notice that luminosity increases upward on the diagram, surface temperature increases to the left, and radius increases diagonally from the lower left to the upper right. Therefore, stars in the upper right must be high in luminosity and radius, but low in surface temperature. ’ These stars are called giants or supergiants because of their large radii. Part C Compared to a low—luminosity main—sequence star, stars in the lower left of the H—R diagram are Hint C.l Which star is hotter? Be sure you have clicked on the "show stars" button and then locate Sirius B (near the lower left) and Ross 128 (near the lower right) in the H-R diagram. True or False? Sirius B has a higher surface temperature than Ross 128. @Be sure you notice that temperature increases to the left on the H—R diagram. Hint C.2 Which star is larger? Be sure you have clicked on the "show stars“ button and then locate Sirius B (near the lower left) and Ross 128 (near the lower right) in the H—R diagram. True or False? Sims B is larger in radius than Ross 128. gBe sure you notice the diagonal lines showing that the smallest radii are found on the lower left on the HR diagram. ANSWER: , hotter and larger in radius i ‘ cooler and larger in radius ' cooler and smaller in radius 1 Q hotter and smaller in radius é Notice that the stars in the lower left of the diagram are called white dwarfs: while because they are hot enough to appear "white hot” to our ‘T eyes, and dwarfs because of their small sizes. A typical white dwarf is no larger in size (radius) than our Earth, but has as much mass as the httpzl/session.masterlngastronomy.com/myct Page 6 of 17 MasteringAstronomy ti Sun. Chapter 17 Multiple Choice Quiz 1 j Description: (a) Which of the following is not an intrinsic property of a star? (b) As the distance of an observed object increases, what does its parallax do? (c) Suppose two stars with the same luminosity are at different distances from Earth. Which has the... Part A Which of the following is not an intrinsic property of a star? Hint A.l ANSWER: An intrinsic property is one that doesn't depend in any way on the location or motion of the observer. E. l Luminosity 1 . Temperature E @Distance Part B As the distance of an observed object increases, what does its parallax do? Hint 8.1 Parallat is an apparent shift of a nearby object relatiVe to background objects due to the changing perspective of the observer. J ANSWER: Stays the same Increases ‘ There is not enough information to answer the question. @.Deereases Yes. As the object moves farther away, its parallav becomes smaller. g Part C Suppose two stars with the same luminosity are at different distances from Earth. Which has the greater apparent brightness? Hint D.l Hint C.1 Apparent brightness is a measure of how bright an object appears; it depends on not only the object's luminosity but also our distance from the object. ANSWER: There is not enough information to answer the question. i @The closer star ' ‘ The farther star I Both have the same brightness. The closer the object, the brighter it will appear. See Section 17.2 in your textbook. g Part D What is the full spectral classification of the Sun? The full spectral classification indicates not only the temperature of a star but also its type. ANSWER: gCorreet. Our Sun is an average-temperature, main-sequence star. See Section 17.6 in your textbook. g Part E Hint E.1 What important property of a star do we learn from its spectral class? The spectral class of a star is determined by its absorption lines. g » r Radius 1 ANSWER: i WTemperature i 5 ‘ Mass Luminosit = gYes. The temperature of a star determines at what wavelengths its atmosphere absorbs photons. See Section 17.3 in your textbook. a Part F A high-mass star has more "fuel" than a low-mass star. Which lives longer? Why? ANSWER: ' The high—mass star lives longer because it has more "fuel to burn" and therefore takes longer to consume it all. ? i The lifetime of a star depends on more than just mass, so not enough infomation is given. httpzl/session.masteringastronomy.com/myct 4/5/10 11:33 AM Page 7 of 17 MasteringAstronomy @ The low—mass star lives longer because, even though it has less "fuel,'I it consumes fuel at a much slower rate than the high~ mass star. The lifetime of a star is independent of mass. Correct. Low-mass stars haVe longer lifetimes. See Section 17.8 in your textbook. Ari H—R diagram is a plot of which two stellar properties? Hliit G.1 Equivalent measures are absolute magnitude and spectral class. ANSWER' Luminosity and mass 1 Brightness and temperature 1 Temperature and mass - Radius and mass 2 @ Luminosrty and temperature“- Yes. An H-R diagram plots luminosity (absolute magnitude) and temperature (spectral class). Part H What property of stars can be measured only by using binary-star systems? Hlnt H.l Consider what property of objects in the solar system can be calculated from orbital information. See Section 17.7 in your textbook for more information on binary-star systems. Magnetic field 9 Mass 3 Temperature . Composition i . Radius Yes. It is possible to use Kepler‘s third law to measure the mass of two objects that orbit around a common center of mass. This method works for stars as well as for planets. See Section 17.7 in your textbook. Part I Which of the following statements about binary-star systems is true? ANSWER: r ’ They all have very long orbital periods (much longer than an Earth year). 3 @They are not the most complex star systems observable; triple, quadruple. and even more complex systems have been found. i They are all too far from Earth to be separated from each other telescopically. l ‘ Their spectral lines are not affected significantly by their mutual orbits. r It is impossible to observe one star actually cross in front of the other. Correct. Most of the star systems in our Galaxy (and probably in most galaxies) are multiple. The Sun, which apparently lacks a companion star 5 ‘ th ' the minority category of singlc~star systems. See Section 17.7 in your textbook. Which of the following methods is useful for determining a star‘s approximate surface temperature? Hint 1.1 Binary-star systems consist of two stars in orbit around a common center of mass. See Section 17.7 in your textbook. Hint J.1 The technique makes use of the blackbody curve discussed in Section 17.3 of the textbook. « Measuring the radius of the star , Measuring the mass of the star 1 Measuring the total energy given of f by the star ; 1 Measuring the temperature of the gas cloud surrounding the star, if one exists g Measurin its a arent bri htness throu h two or more color filters and com arin these values i... l i x 2%? Correct. As shown in Figure 17.9 and discussed in Section 17.3, as few as two brightness measurements at different wavelengths can be used to g determine the effective blackbody temperature of a star. Part K Our Sun is classified as a G2 star. Vega, which is 26.4 light—years away, is an A0 star, and Bamard's Star is type M5. How do these stars compare in terms of temperature? Hint K.1 The letters in these designations indicate the spectral class, and the numbers divide each class into 10 finer subdivisions. Recall the mnemonic from the text that gives the order in which these spectral classes are arranged. x @Vega is hotter than the Sun, w ch in turn is hotter than Bamard's Star. l 1 v To answer this question, We need to know the distance to Bamard's Star as well. Z ’ Vega is cooler than the Sun, which in turn is cooler than Bamard's Star. ‘ . The Sun is cooler than Vega, which in turn is cooler than Bamard's Star. he Sun is hotter than Ve a wh‘ch~ t ' hott th B d' Part L http:/[session.masteringastronomy.com/myct 4/5/10 11:33 AM Page 8 of 17 MasteringAstronomy 4/5/10 11:33 AM What property of a star does the magnitude scale measure? Hint L.1 Refer to Section 17.2 in your textbook for more information. : 9 Apparent brightness ; I TMass . ' Temperature Which stars are most common in the Galaxy? Hint M.l Refer to Section 17.5 in your textbook for more information. ANSWER! White dwarfs i ‘ » O- and B«type main-sequence stars 2 @Red dwarfs : 1 Red giants i t l r r i r 2 Ekorrect. Red dwarfs account for about 80 percent of stars in the Galaxy. Refer to Section 17.5 in your textbook for more information. Part N In spectroscopic parallax, a star‘s spectral type and what other property are used to determine an approximate distance? Refer to Section 17.6 in your textbook for more information. ANSWER: Composrtron 1 Radial velocity ‘ Luminosity class @Apparent brightness Correct. A star's apparent brightness and spectral type are used to determine its distance. Luminosity can be inferred from the H-R diagram when the spectral type is known if the star is a main»sequence star. Refer to Section 17.6 in your textbook for more information. Which main~sequence star spectral type has the shortest lifetime? Hint 0.1 Refer to Section 17.8 in your textbook for more information. ANSWER- Correct. Refer to Section 17.8 in your textbook for more information. Problems 17.5 Description: Two stars < A and B, with luminosities L_1 and LgZ times the luminosity of the Sun, respectively » are observed to have the same apparent brightness. (a) Which star is more distant? (b) How much farther away is it than the other? Two stars ~ A and B, with luminosities 1.2 and 4.8 times the luminosity of the Sun, respectively - are observed to have the same apparent brightness. Part A Which star is more distant? frat-t B How much farther away is it than the other? Express your answer using two significant figures. ANSWER: Ranking Task: The Life of a Low-Mass Main-Sequence Star Description: A ranking task to ensure that students know the correct sequence of the key stages in the life of a low—mass star, and where on the HR diagram the star appears at key stages. Part A httpzl/session.masteringastronomy.com/myct Page 9 of 17 MasteringAstronomy The following figures show various stages during the life of a star with the same mass as the Sun. Rank the stages based on when they occur, from first to last. Hint A.l What is a main-sequence star? A main-sequence star is Qa star in the longest stage of its life, in which it IS fustng hydrogen into helium in liS core a star that has not yet been “bom” a star nearing the end of its life, when it has exhausted its core supply of hydrogen ANSWER: gWith this fact in mind, you should be off to a good start on the ranking task in Part A. Hint A.2 What is a protostar? Protostar is the name we give to ANSWER: a star with a strong stellar wind i ‘a star that has recently died @a star that has not quite reached its “birth,” meaning its core is not yet hot enough to sustain nuclear fusion aYou should now be able to rank the protostar stage correctly. Hint A.3 What makes a red giant shine? A red giant shines with energy released by > z (D S re 2? é’hydrogen fusion in a shell surrounding an inert helium core ' gravitational contraction the ejection of the star's outer layers into space géva, remember that hydrogen shell burning occurs only after the star has exhausted its core supply of hydrogen g Hint A.4 What is a white dwarf? A white dwarf is @the dead remains of a low~mass star I a star that has not yet been "born" a hot star that is fusing hydrogen into helium in its core ANSWER: Assume that the four H-R diagrams below all Show the same one-solar-mass star at different stages in its life. Rank the HR diagrams based on when each stage occurs, from first to last. Hint B.l Where do we find giant stars on the H-R diagram? On the H-R diagram, red giants are found in the lower left, where stars are dim but hot on the strip that extends from the upper left to the lower right 1: sequence but not yet become giants are subgiants, so subgiant stage precedes red giant stage. Hint 13.2 Where do we find white dwarfs on the H—R diagram? On the H—R diagram, white dwarfs are found ANSWER: ‘ toward the upper right, where stars are bright but cool 3 fin the lower left, where stars are dim but hot on the strip that e tends from the upper left to the lower right gNow, remember that a white dwarf is the dead remnant of a low-mass star. ANSWER: i http2//session.masteringastronomy.com/myct 4/5/10 11:33 AM Page 10 of 17 MasteringAstronomy x i i i i i I i i i i i i i i i l i The diagram at the left represents the Sun (or any other one-solar—mass star) as a hydrogen-burning main-sequence star, with spectral type G and one solar luminosity. The next diagram shows the Sun after it has exhausted its core hydrogen and ief t the main sequence, making it a subgiant with energy generated by hydrogen buming in a shell around an inert helium core. The third diagram shows the Sun a little later; its energy source is still hydrogen shell burning, but at this point it has expanded in size so much that it is a red giant. The final diagram (far right) shows the white dwarf corpse of a onesolar-mass star; it is hot because it is the exposed core of the dead star, but dim because it can no longer generate energy by fusion. a ‘ oasmaraawam, .i S\ Sorting Task: High- and Low-Mass Star's :Description: A sorting task challenging students to compare low—mass and high-mass stars. Part A Listed following are characteristics that describe either high-mass or low-mass stars. Match these characteristics to the appropriate category. Hint A.l A strategy for completing this task The only way to complete this sorting task successfully is to know the different ways in which low—mass and high~mass stars live their lives. To get started on this task, first remember that high-mass stars proceed through all their life stages in a much shorter time than low—mass stars. Second, remember that most of the elements of which we and Earth are made were produced by fusion in high-mass stars. Beyond that, you'll need to review the life stages of low— and high-mass stars as discussed in our textbook. Description: (a) In a white dwarf, what is the source of pressure that halts its contraction? (b) Algol is a binary system that consists of a B8 main— ‘ sequence star and a 0.8-solar-mass red-subgiant companion. How do astronomers explain the evolution of Algol? (... _‘ Part A In a white dwarf, what is the source of pressure that halts its contraction? Hint A.1 A white dwarf no longer generates energy via fusion, so something else must balance the force of gravity. ANSWER: Neutrons that resist being pressed further together i g ' 3 Normal thermal pressure of the hot gas i @Electrons packed so closely that they become incompressible i arbon nuclei that re ulse each othe st 0 l ' beca Part B Algol is a binary system that consists of a BS main»sequence star and a 0.8-solar-mass red-subgiant companion. How do astronomers explain the evolution of Algol? Hint B.l Y—mass star. How does the evolution of a star depend on its mass? A BS star is a massive star and a 0 8 olar-mass star is a lo ANSWER: “ ‘ ‘ There is nothing out of the ordinary in this situation. I The two stars must have formed separately and become gravitationally bound to each other at a later date. : . r The 138 star gravitationally pulled mass from its companion star, forcing its companion to evolve faster than it normally would. : fiThe subgiant star must have been more massive in the past, evolved faster, and funneled some of its mass onto its companion t 5 star. 3 Yes. When two stars are close enough, material from one star can flow onto the other, altering the evolution of both stars. See Section 20.6 in ; your textbook. Part C What is the primary composition of a white dwarf? 'nt C.l Up to what element did the original star fuse at the point that it became a white dwarf? http://session.masteringastronomy.com/myct 4/5/10 11:33 AM Page 11 of 17 MasteringAstronomy 4/5/10 11:33 AM ANSWER: l acme“ i ~ Hydrogen i 3 Oxygen Helium S’l' ‘ Fusion in low-mass stars ends at carbon. See Section 20.3 in your textbook. Ag Part D What is the age range among the globular clusters associated with our Galaxy? Hint D.l Distinguish carefully betWeen the globular clusters described in this chapter and the open clusters discussed in Chapter 19 in your textbook. ANSWER: The globular clusters range from 5 to 15 billion years old. All the globular clusters formed during the time period between I and 2 billion years ago. x The globular clusters range from 2 to 8 billion years old. @All the globular clusters formed during the time period between 10 and 12 billion years ago. ‘ ‘ Th 1 b l l sters ang fro 100 mill‘ to 2 billion years old. i i i s s i ElYes. The globular clusters are associated with the early stages of galaxy formation. We will discuss this further in Chapter 23 in the textbook. Part E What is a planetary nebula? Hint E.l See Figure 20.10 in your textbook for the structure of a planetary nebula. ANSWER: Neither a planet nor a nebula ‘ A forming planetary system @An expanding shell of gas around a white dwarf star 5 '- ‘ A spherical dust cloud falling into a star A cloud of gas around a planet A planetary nebula looks vaguely like a planet through a telescope. Part F In its last stage of evolution, what will the Sun become? Hint F.1 Which of the choices has a mass comparable to that of the Sun but does not generate new energy? ANSWER: ‘ Planetary nebula _ Supemova @White dwarf 1 i Red giant Red supergiant es. The Su will end its evolution as a white dwarf . which will slowly cool to become a black dwarf. What is the main-sequence (hydrogen core-buming) lifetime for stars like the Sun‘] Hint 0.1 What is the projected life span for the Sun? ANSWER: , 10 million years ® 10 billion years 5 f 1 trillion years 300 million years Part H What is the size of the core of a typical white dwarf star? Hint H.l Consider that the star would have lost some material in ejecting a planetary nebula and the remaining core would have become denser. See Section 20.3 in your textbook. ANSWER= . »About the size of our entire solar system @About the size of Earth Many times the size of our Sun About the size of our Sun About the size of an asteroid % Correct. In some cases, the white dwarf remnant is even smaller than Earth. See Section 20.3 in your textbook. Part I Which of the following sequences is correct for the five stages of evolution of a 1-solar-mass star like our Sun just after it leaves the main sequence? [Him 1.1 » ........... as. _W «I http://session.masteringastronomy.com/myct Page 12 of 17 MasteringAstronomy Such a star could eventually bum helium, but it would be too small and cool to fuse carbon in its core. A - Red giant, vertical branch, red supergiant, horizontal branch, white dwarf ‘ Red giant, helium flash, vertical branch, subgiant, supemova f White dwarf, red giant, helium flash, horizontal branch, black dwarf @Subgiant, red giant, helium flash, horizontal branch, asymptotic giant branch ‘ ANSWER: : @Correct. This sequence is described in Table 20.1 and the accompanying discussion in your textbook. Part J Which of the following statements is true for the Hertzsprung-Russell diagram of an isolated star cluster approximately 1 billion years old? Hint J.l Most globular clusters have essentially no stars larger 1 solar mass that remain on the main sequence, How old would a cluster have to be for this to occur? ANSWER: It would be depleted of O- and B-type stars from the main sequence, with all other stars occupying the main sequence or ept ® for a few white dwarfs. , It would show most stars on the zero-age main sequence, but with some small stars not yet on it and a few O-type stars that 5 ' ' had evolved off of it. . It would lack stars larger than 1 or 2 solar masses from the main sequence, with distinct subgiant, red giant, and horizontal branch populations in evidence and a significant number of white dwarfs. , It would show essentially all stars larger than 1 solar mass to be on the zero-age main sequence, but smaller stars would not yet I have evolved onto it. i , It would show a distinct turnoff from the main sequence of hi gh-mass stars, with essentially all other stars on or near the zer0< ' ' age main sequence E Correct. Part K Which of the following sequences is correct for the last four stages of evolution of an isolated 1-solar-mass star like our Sun, as identified in the textbook? Hint K] The evolution of an isolated l-solar~mass star like our Sun is not affected by the presence of another star as a binary companion. See Table 20.1 in your textbook. » 3 Horizontal branch, carbon core + planetary nebula, helium flash, black dwarf 3 Red giant, carbon core + planetary nebula, white dwarf, black dwarf _ Supemova, carbon core + planetary nebula, white dwarf, black dwarf g 1 ‘ Red giant, planetary nebula, helium core, brown dwarf r Blue giant, horizontal branch, red giant, white dwarf ANSWER: Correct. See Table 20.1 in your textbook. Part L While a star is on the main sequence, its equilibrium is the result of the outward pressure of hot gas and the inward pressure of Hint L.l Refer to Section 20 l in your textbook for more information. ANSWER: g gm, y radiation pressure ‘ ‘ degenerate electron pressure , convection g Correct. All the other choices produce outward pressures. Refer to Section 20.1 in your textbook for more information. Part M How big, in solar radii, will the Sun become when it is a mature red giant? Hint M.1 Refer to Section 20.2 in your textbook for more information. ANSWER: Correct. Refer to Section 20.2 in your textbook for more information. Part N How long does it take for a star like the Sun to evolve from the main sequence to the top of the red-giant branch? Hint N.l tion 20.2 in your textbook for more information. 9 100 million years i I ‘ About 10 billion years i ‘ ' About 1 billion years i i A few tens of millions of years httpzl/session.masteringastronomy.com/myct 4/5/10 11:33 AM Page 13 of 17 MasteringAstronomy 9 Correct. Though long in human terms, 100 million years is only a few percent of the Sun's main-sequence lifetime. Refer to Section 20.2 in your textbook for more information. What is the stage of relative stability in a. solar-mass star when it fuses helium into carbon? Hiiit 0.1 Refer to Section 20.2 in your textbook for more information. ANSWER: : 1 Lower main sequence i ' r Red-giant branch ‘ g i » Subgiant branch @Horizontal branch 5 Correct. Refer to Section 20.2 in your textbook for more information. E Chapter 20 Multiple Choice Quiz 2 Description: (a) How do astronomers explain the existence of “blue stragglers"? (b) When a star depletes its core supply of hydrogen, dominates in the core and dominates in the envelope. (0) Hydrogen~shell burning proceeds increasingly... Part A How do astronomers explain the existence of “blue stragglers"? Hint A.l Blue stragglers are stars on a cluster H-R diagram that lie above the main-sequence turnoff point. 1 ’ They are stars that formed elsewhere and are a different age but were gravitationally captured by the cluster. f They are main~sequence stars whose evolution has been altered by mergers or binary companions, causing them to live longer than usual for a star of their spectral type. , . They are stars that appear to lie along the main sequence but that have actually evolved off the horizontal branch on their way ‘ i to becoming white dwarfs. ' Astronomers are unable to e l i . . . ; lain the ongm of blue stragglers. Correct. Astronomers believe that in dense clusters, mergers and close binaries are common and can affect the evolution rate of stars. See 5 Section 20.3 and Figure 20.20 in Section 20.5 in your textbook. Part B When a star depletes its core supply of hydrogen, dominates in the core and dominates in the envelope. Hint 3.1 If energy isn't being generated in the core, what force dominates? Energy is being generated in a shell layer around the core, so what dominates there? ANSWE pressure; pressure @giavity; pressure ‘ gravity; gravity ' pressure' gravity §Yes The core contracts due to gravity, while the envelope swells due to radiation pressure. See Section 20.2 in your textbook. E Part C Hydrogen-shell burning proceeds increasingly faster due to which of the following? Hint C.l Conditions need to bejust right for protons to come close enough to one another to overcome their electromagnetic repulsion and fuse together. ANSWER' » Rotational energy from the star's rapid rotation ‘. Pressure from the contracting envelope 3 Heat released from the cores contraction ' This is a trick questio Hydrogen actually burns increasingly slower with time g Yes. Higher temperatures cause the protons to move faster, so that they interact more often and fuse at a faster rate. See Section 20.2 in your textbook. Part D As a low-mass main~sequence star runs out of fuel in its core, it actually becomes brighter. How is this possible? Hint D.1 According to the radius-luminosity-temperature relationship, the luminosity of a star depends not only on its temperature but also on its size. The outer layers pand due to the high rate of fusion in a shell around the dead core. 1 . ‘ It immediately starts to fuse helium. ' » It explodes. ‘ Its outer envelope is stripped away, and we Start to see its bright core. ANSWER' i gYes. See Section 20.2 in your textbook. Part E When is a star on the asymptotic giant branch of the H—R diagram? {Hint E.1 httpz//sesslon.masteringastronomy.com/myct 4/5/10 11:33 AM Page 14 of 17 MasteringAstronomy 4/5/10 11:33 AM Befer to Table 20.1 in your textbook. ANSWER: : When the core is collapsing before the helium flash When it is in the planetary nebula stage ‘ When hydrogen fusion begins i Q After the horizontal branch 3 1 Immediately after the helium flash @Yes. In the asymptotic giant branch, the carbon core grows in mass. Part F Which of the following stars has the highest density? Hint F.1 All of these stars can have similar masses. Which has the smallest volume? ANSWER: ‘ Main—sequence star » Red giant Supergiant t Subgiant @ White dwarf E3 Yes. A white dwarf, at about half the mass of the Sun and the size of Earth, is by far the densest of the stars listed. Part G Why don't stars live foreVer'I Hint G] What is the energy source for stars? ANSWER: v ‘ They run out of oxygen long before they run out of fuel, so they stop shining. Q They run out of nuclear fuel in their cores. 3 Their cores cool off and fusion stops. ‘ Th ' all th ' h d What is the helium flash? Hint H.1 When does a star begin fusing helium into heavier elements? ANSWER: A type of flare that occurs on the surface of solar-type stars 1 3 The explosion that creates a planetary nebula i ’ ‘ The flash of light given off when a star collapses into a white dwarf QThe rapid fusion of helium in the electron-degenerate helium core of a red giant Yes. This marks the end of the stasz expansion along the giant branch. Part I What is the region of the Hertzsprung-Russell diagram known as the horizontal branch? See Section 20.2 in your textbook. It is the track that low~mass stars follow between the helium flash and the time their planetary nebula is ejected. It is the track that Sun-like stars follow as they evolve off the main sequence, before the helium flash. It is the path in the H-R diagram that white dwarf stars follow as they age. It is the track followed by high-mass stars as they undergo progressive fusion of different nuclei. @It is a region of the H—R diagram where stars remain for a time as they undergo helium core fusion g Correct. This region is discussed in Section 20.2 of your textbook. Part J Why is the depletion of hydrogen in the core of a star such an important event? Hint J.1 Refer to Section 20.2 in your textbook for more information. ANSWER X It means the star is going to die immediately. * ‘ The star will begin to produce less and less energy until it becomes a black dwarf. ! @I‘he star will begin to change its structure drastically. ; l ’ ‘ The star is about to explode. E Correct. The star will change into a red giant. Refer to Section 20.2 in your textbook for more information. 3“ M .m M-” __,.__.... . .M Part K What is a contact binary? Hint K.1 Refer to Section 20.3 in your textbook for more information. http://session.masteringastronomy.com/myct Page 15 of 17 MasteringAstronomy _ a Two stars that are close enough together to transfer mass t @Two nuclear-buming stellar cores surrounded by a single continuous common envelope i 1_. Two stars with Roche lobes that meet at a point on the line joining them i ‘ ' Any binary system within communications distance of Earth ANSWER: orrect. Refer to Section 20.6 in your textbook for more information. Part L Which of the following is not a property of a white dwarf? Hint L.1 Refer to Section 20.3 in your textbook for more information ANSWER: ~ I High surface temperature @Mass equivalent to 1 percent of the Sun‘s mass 2 . Density higher than any other star in the H-R diagram ' Size similar to that of the Earth . Correct. A white dwarfs mass is about half the mass of the Sun. Refer to Section 20.3 in your textbook for more information. Part M At what stage do the evolutions of high— and low-mass stars diverge? Hint M.l Refer to Section 20.4 in your textbook for more information. ANSWER: i After hydrogen-shell burning g Immediately after the main sequence 5 3 During the main sequence i @After the formation of a carbon core Correct. Low-mass stars cannot continue burning nuclear fuels after the formation of a carbon core. Refer to Section 20.4 in your textbook for more information. Part N What property of a star cluster helps determine its age? Hint N.1 Refer to Section 20.5 in your textbook for more information. ‘ ANSWER: The number of white dwarfs in the cluster 3 I - The number of stars in the cluster i @ Main-sequence turnoff The t of cluster Correct. Refer to Section 20.5 in your textbook for more inf onnation. Part 0 Use the radius-luminosity—temperature relationship (L ~ R 2 x T 4; see Section 17.4 in your textbook) to calculate the radius of a red supergiant with a temperature of 3000 K (half the solar value) and a luminosity of 10,000 solar luminosities. Hint 0.] Refer to Sections 17.4 and 20.4 in your textbook for more information. ANSWER: i 25 solar radii é ‘ 160,000 solar radii g @400 solar radii ' ' 625 solar radii ns 17.4 and 20.4 in your textbook for more information. % Eblems 20.2 Description: (21) Use the radiusvluminosity-temperature relation to calculate the radius of a red supergiant with temperature 3000 K (half the solar value) and total luminosity L times that of the Sun. (Sec. 17.3 in the textbook)... (b) How many planets of our... Use the radius-luminosity—temperature relation to calculate the radius of a red supergiant with temperature 3000 l\' (half the solar valu/ef'and total luminosity 50000 times that of the Sun. (Sec. 17.3 in the textbook) , I ‘ Express your answer using two significant figures. ' W ' ’ ’1' F > w 0.00101 in ‘JL a? 3 it 0m in MAE Part B httpzl/session.masteringastronomy.com/myct 4/5/10 11:33 AM MasteringAstronomy 4/5/10 11:33 AM How many planets of our solar system would this slar engulf? *' Express your answer as an integer. %LMa/m 84W fill/g. ANSWER: Score Summary: Your score on this assignment is 313%. You received 1.06 out of a possible total of 5 points, plus 0.52 points of extra crediL http://session.masteringastronomy.com/myct Page 17 of 17 ...
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This note was uploaded on 03/31/2011 for the course ASTRO 102 taught by Professor P during the Spring '11 term at Arizona.

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