UNDERSTANDING THE UNIVERSE(LL)-W/CODE
3rd Edition
ISBN: 9780393869903
Author: PALEN
Publisher: NORTON
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Chapter 12, Problem 29QAP
To determine
The indication given by increase in luminosity of star when it leaves main-sequence phase.
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The mass-luminosity relation describes the mathematical relationship between luminosity and mass for main sequence stars. It describes how a star with a mass of 4 M⊙ would have a luminosity of ______ L⊙.
If a star has a radius 1/2 that of the Sun and a temperature 4 that of the Sun, how many times higher is the star's luminosity than that of the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125)
If a star has a radius 2 times larger than the Sun's and a luminosity 1/4th that of the Sun, how many times higher is the star's temperature than that of the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125)
If a star has a surface temperature 2 times lower than the Sun's and a luminosity the same as the Sun, how many times larger is the star than the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125)
Using solar units, we find that a star has 4 times the luminosity of the Sun, a mass 1.25 times the mass of the Sun, and a surface temperature of 4090 K (take the Sun's surface temperature to be 5784 K for the sake of this problem). This means the star has a radius of.................... solar radii and is a .................... star (use the classification).
For a main sequence star with luminosity L, how many kilograms of hydrogen is being converted into helium per second? Use the formula that you derive to estimate the mass of hydrogen atoms that are converted into helium in the interior of the sun (LSun = 3.9 x 1026 W).
(Note: the mass of a hydrogen atom is 1 mproton and the mass of a helium atom is 3.97 mproton. You need four hydrogen nuclei to form one helium nucleus.)
Chapter 12 Solutions
UNDERSTANDING THE UNIVERSE(LL)-W/CODE
Ch. 12.1 - Prob. 12.1CYUCh. 12.2 - Prob. 12.2CYUCh. 12.3 - Prob. 12.3CYUCh. 12.4 - Prob. 12.4CYUCh. 12.5 - Prob. 12.5CYUCh. 12.6 - Prob. 12.6CYUCh. 12 - Prob. 1QAPCh. 12 - Prob. 2QAPCh. 12 - Prob. 3QAPCh. 12 - Prob. 4QAP
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- The text says a star does not change its mass very much during the course of its main-sequence lifetime. While it is on the main sequence, a star converts about 10% of the hydrogen initially present into helium (remember it’s only the core of the star that is hot enough for fusion). Look in earlier chapters to find out what percentage of the hydrogen mass involved in fusion is lost because it is converted to energy. By how much does the mass of the whole star change as a result of fusion? Were we correct to say that the mass of a star does not change significantly while it is on the main sequence?arrow_forwardQUESTION 16 Use the figure shown below to complete the following statement: A low-mass protostar (0.5 to 8M the mass compared to our sun) remains roughly constant in decreases in until it makes a turn towards the main sequence, as it follows its evolutionary track. Protostars of different masses follow diferent paths on their way to the main sequence. 107 Luminosity (L) 10 105 10 107 10² 101 1 10-1 10-2 10-3 Spectral type 0.01 R 0.001 Re 60 M MAIN SEQUENCE 40,000 30,000 20 Mau 10 Mgun 5 Mun 0.1 Run Ren radius; temperature luminosity; radius 3 Min. 05 BO temperature; luminosity Oluminosity: temperature radius: luminosity 1 M 10,000 6000 Surlace temperature (K) 1,000 Rs 2 M STAR L 0.8 M B5 AO FOGO КБ МБ -10 +10 3000 Absolute visual magnitude andarrow_forwardObservations show that stellar luminosity, L, and mass, M, are related by L x M3.5 for main sequence stars. Obtain an expression that relates the main sequence life time and the mass of a star. You should assume that the luminosity is constant throughout a star's main sequence life time, and that the amount of mass converted into energy by a star while it is on the main sequence is given by AM main sequence life time of a 20 Solar mass star given that the Sun is expected to spend 1010 years on the main sequence. Comment on the significance of your answer. fM, where f is a constant. Estimate thearrow_forward
- This star has a mass of 3.3 MSun. What is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr.arrow_forwardSelect all of the statements about the main sequence stage in the life of a star that are TRUE: All stars spend the majority of their lives in the main sequence stage. Most stars lose a significant amount of mass while they are on the Main Sequence. Different stars spend a different amounts of time (number of years) in the main sequence stage, depending on the characteristics they were born with. Main sequence stars are rare in the Galaxy, so we are lucky to be living around one. During the main sequence stage, energy to power the star is provided by the fusion of hydrogen.arrow_forward12: A star with spectral type A0 has a surface temperature of 9600 K and a radius of 2.2 RSun. How many times more luminous is this star than the Sun? (if it is less luminous enter a number less than one) Answer: 36.854 13:This star has a mass of 3.3 MSun. what is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr. Please answer question 13 thank you.arrow_forward
- According to the text, a star must be hotter than about 25,000 K to produce an H II region. Both the hottest white dwarfs and main-sequence O stars have temperatures hotter than 25,000 K. Which type of star can ionize more hydrogen? Why?arrow_forwardDescribe what happens when a star forms. Begin with a dense core of material in a molecular cloud and trace the evolution up to the time the newly formed star reaches the main sequence.arrow_forwardIf you were to compare three stars with the same surface temperature, with one star being a giant, another a supergiant, and the third a main-sequence star, how would their radii compare to one another?arrow_forward
- Describe the evolution of a star with a mass similar to that of the Sun, from the protostar stage to the time it first becomes a red giant. Give the description in words and then sketch the evolution on an HR diagram.arrow_forwardIf a 100 solar mass star were to have a luminosity of 107 times the Sun’s luminosity, how would such a star’s density compare when it is on the main sequence as an O-type star, and when it is a cool supergiant (M-type)? Use values of temperature from Figure 18.14 or Figure 18.15 and the relationship between luminosity, radius, and temperature as given in Exercise 18.47. Figure 18.15 Schematic HR Diagram for Many Stars. Ninety percent of all stars on such a diagram fall along a narrow band called the main sequence. A minority of stars are found in the upper right; they are both cool (and hence red) and bright, and must be giants. Some stars fall in the lower left of the diagram; they are both hot and dim, and must be white dwarfs. Figure 18.14 HR Diagram for a Selected Sample of Stars. In such diagrams, luminosity is plotted along the vertical axis. Along the horizontal axis, we can plot either temperature or spectral type (also sometimes called spectral class). Several of the brightest stars are identified by name. Most stars fall on the main sequence.arrow_forwardLook at the four stages shown in Figure 21.8. In which stage(s) can we see the star in visible light? In infrared radiation? Figure 21.8 Formation of a Star. (a) Dense cores form within a molecular cloud. (b) A protostar with a surrounding disk of material forms at the center of a dense core, accumulating additional material from the molecular cloud through gravitational attraction. (c) A stellar wind breaks out but is confined by the disk to flow out along the two poles of the star. (d) Eventually, this wind sweeps away the cloud material and halts the accumulation of additional material, and a newly formed star, surrounded by a disk, becomes observable. These sketches are not drawn to the same scale. The diameter of a typical envelope that is supplying gas to the newly forming star is about 5000 AU. The typical diameter of the disk is about 100 AU or slightly larger than the diameter of the orbit of Pluto.arrow_forward
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