21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 17, Problem 19QP
To determine
The two reasons why each post-helium-fusion cycle for high-mass stars becomes shorter than the preceding cycle.
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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)
When two stars are in the same star system, they can affect each other’s evolution. Two stars in the same system might be born at the same time, but they will evolve at a different pace, depending on their _________. Transfer of material between two stars in the same system can be especially dramatic if one star is __________. When one star transfers mass to the remnant that is the other star, it can re-ignite fusion and produce what astronomers call a _________. If the accumulated mass causes the remnant to have a mass greater than ____________, it can explode violently. Astronomers call this kind of explosion a ________________.
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 17 Solutions
21st Century Astronomy
Ch. 17.1 - Prob. 17.1CYUCh. 17.2 - Prob. 17.2CYUCh. 17.3 - Prob. 17.3CYUCh. 17.4 - Prob. 17.4CYUCh. 17 - Prob. 1QPCh. 17 - Prob. 2QPCh. 17 - Prob. 3QPCh. 17 - Prob. 4QPCh. 17 - Prob. 5QPCh. 17 - Prob. 6QP
Ch. 17 - Prob. 7QPCh. 17 - Prob. 8QPCh. 17 - Prob. 9QPCh. 17 - Prob. 10QPCh. 17 - Prob. 11QPCh. 17 - Prob. 12QPCh. 17 - Prob. 13QPCh. 17 - Prob. 14QPCh. 17 - Prob. 15QPCh. 17 - Prob. 16QPCh. 17 - Prob. 17QPCh. 17 - Prob. 18QPCh. 17 - Prob. 19QPCh. 17 - Prob. 20QPCh. 17 - Prob. 21QPCh. 17 - Prob. 22QPCh. 17 - Prob. 23QPCh. 17 - Prob. 24QPCh. 17 - Prob. 25QPCh. 17 - Prob. 26QPCh. 17 - Prob. 27QPCh. 17 - Prob. 28QPCh. 17 - Prob. 29QPCh. 17 - Prob. 30QPCh. 17 - Prob. 31QPCh. 17 - Prob. 32QPCh. 17 - Prob. 33QPCh. 17 - Prob. 34QPCh. 17 - Prob. 35QPCh. 17 - Prob. 36QPCh. 17 - Prob. 37QPCh. 17 - Prob. 38QPCh. 17 - Prob. 39QPCh. 17 - Prob. 40QPCh. 17 - Prob. 41QPCh. 17 - Prob. 42QPCh. 17 - Prob. 43QPCh. 17 - Prob. 44QPCh. 17 - Prob. 45QP
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- In a star of 1 solar mass (M☉), the core hydrogen burning phase, also known as the main sequence phase, lasts for approximately 10 billion years. Suppose there's a star of 15 solar masses (M☉). Stars of higher mass burn through their hydrogen at a faster rate, following an approximate relation that the lifetime of a star on the main sequence (T) is proportional to its mass (M) raised to the power of -2.5 (T ∝ M^-2.5). Calculate approximately how long this 15 solar mass star would remain in the main sequence phase, compared to the 1 solar mass star.arrow_forwardAssuming that at the end of the He burning phase of the stellar core (r < R_core) has no H or He or other metals and is composed completely of Carbon, X=Y=0, X_c = 1 ; The envelope above the core has a normal stellar composition ( r > R_core). Calculate the length of time in years that a 1M_sol and 10M_sol star will live on the horizontal branch or the time between the start and end of the He burning phase. Assume that the normal relationship between mass and luminosity holds for horizontal branch stars. Please be as detailed as possiblearrow_forwardWhat are the main products of the fusion reactions that take place in low mass main sequence stars?arrow_forward
- Place the following events in the formation of stars in the proper chronological sequence, with the oldest first and the youngest last. w. the gas and dust in the nebula flatten to a disk shape due to gravity and a steadily increasing rate of angular rotation x. a star emerges when the mass is great enough and the temperature is high enough to trigger thermonuclear fusion in the core y. the rotation of the nebular cloud increases as gas and dust concentrates by gravity within the growing protostar in the center z. some force, perhaps from a nearby supernova, imparts a rotation to a nebular cloud y, then z, then w, then x z, then y, then w, then x w, then y, then z, then x z, then x, then w, then y x, then z, then y, then w MacBook Air on .H. O O O Oarrow_forwardQuestion 41 .Suppose you are looking at H-R diagrams of two similar star clusters. The most luminous main sequence stars in the Porcini cluster are much more luminous than the most luminous main sequence stars in the Morel cluster. What can you conclude? O the Porcini cluster is younger than the Morel cluster O the Porcini cluster is farther away than the Morel cluster O the Porcini cluster is lower in metallicity than the Morel cluster O the Porcini cluster is larger in diameter than the Morel clusterarrow_forwardA main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say “mass vanish '' what we really mean is “gets converted into energy and leaves the star as light”. Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.arrow_forward
- A red giant star might have radius = 104 times the solar radius, and luminosity = 1730 times solar luminosity. Use the data given below to calculate the temperature at the surface of the red giant star. Data: solar radius R = 7 x 108 meters solar luminosity L = 4 x 1026 watts Stefan-Boltzmann constant a = 5.67 x 10-8 W m² K-4 (in K) A: 1226 OB: 1434 OC: 1678 OD: 1963 OE: 2297 OF: 2688 OG: 3145 OH: 3679arrow_forwardUsing 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).arrow_forwardConsider an M-dwarf star of mass 0.1M⊙ and luminosity 10−3L⊙. When the star joins the main sequence 75% of its mass is hydrogen and 25% is helium. The star is fully convective and hence the interior is always fully mixed. Fusion reactions provide all of the luminosity of the star, and each reaction converts 4 hydrogen nuclei into 1 helium nucleus. The combined mass of 4 hydrogen nuclei is 6.690×10−27kg and the mass of one helium nucleus is 6.643×10−27kg. Estimate the main sequence life time of this star, assuming that the luminosity is constant throughout the star's life time. Express your answer in Gyr. The solar mass M⊙=2×1030kg and the solar luminosity L⊙=3.83×1026W.arrow_forward
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