21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 15, Problem 43QP
To determine
Estimate the size of a protostar and compare with the size of Sun.
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Students have asked these similar questions
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)
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.)
QUESTION 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
and
Chapter 15 Solutions
21st Century Astronomy
Ch. 15.1 - Prob. 15.1CYUCh. 15.2 - Prob. 15.2CYUCh. 15.3 - Prob. 15.3CYUCh. 15.4 - Prob. 15.4CYUCh. 15 - Prob. 1QPCh. 15 - Prob. 2QPCh. 15 - Prob. 3QPCh. 15 - Prob. 4QPCh. 15 - Prob. 5QPCh. 15 - Prob. 6QP
Ch. 15 - Prob. 7QPCh. 15 - Prob. 8QPCh. 15 - Prob. 9QPCh. 15 - Prob. 10QPCh. 15 - Prob. 11QPCh. 15 - Prob. 12QPCh. 15 - Prob. 13QPCh. 15 - Prob. 14QPCh. 15 - Prob. 15QPCh. 15 - Prob. 16QPCh. 15 - Prob. 17QPCh. 15 - Prob. 18QPCh. 15 - Prob. 19QPCh. 15 - Prob. 20QPCh. 15 - Prob. 21QPCh. 15 - Prob. 22QPCh. 15 - Prob. 23QPCh. 15 - Prob. 24QPCh. 15 - Prob. 25QPCh. 15 - Prob. 26QPCh. 15 - Prob. 27QPCh. 15 - Prob. 28QPCh. 15 - Prob. 29QPCh. 15 - Prob. 30QPCh. 15 - Prob. 31QPCh. 15 - Prob. 32QPCh. 15 - Prob. 33QPCh. 15 - Prob. 35QPCh. 15 - Prob. 36QPCh. 15 - Prob. 37QPCh. 15 - Prob. 38QPCh. 15 - Prob. 39QPCh. 15 - Prob. 40QPCh. 15 - Prob. 41QPCh. 15 - Prob. 42QPCh. 15 - Prob. 43QPCh. 15 - Prob. 44QPCh. 15 - Prob. 45QP
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- 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_forwardA protostar evolves from a temperature T = 3500 K and a luminosity L = 5000 times that of the Sun to T = 5000 K and L = 3 solar units. What is its radius (a) at the start, and (b) at the end of the evolution? (need full step)arrow_forwardOne way to calculate the radius of a star is to use its luminosity and temperature and assume that the star radiates approximately like a blackbody. Astronomers have measured the characteristics of central stars of planetary nebulae and have found that a typical central star is 16 times as luminous and 20 times as hot (about 110,000 K) as the Sun. Find the radius in terms of the Sun’s. How does this radius compare with that of a typical white dwarf?arrow_forward
- A planetary nebula expanded in radius 0.3 arc seconds in 30 years. Doppler measurements show the nebula is expanding at a rate of 35 km/s. How far away is the nebula in parsecs? First, determine what distance the nebular expanded in parsecs during the time mentioned. Δd = vpc/sTs So we first need to convert the rate into pc/s and the time into seconds: vpc/s = vkm/s (1 pc / 3.09 x 1013km) vpc/s = ? Ts = (Tyr)(365 days/yr)(24 hrs/day)(3600 s/hr) Ts = ? s Δd= vpc/sTs Therefore, Δd = ? pcarrow_forwardBetelgeuse is a nearby supergiant that will eventually explode into a supernova. Let's see how awesome it would look. At peak brightness, the supernova will have a luminosity of about 10 billion times the Sun. It is 600 light-years away. All stellar brightnesses are compared with Vega, which has an intrinsic luminosity of about 60 times the Sun, a distance of 25 light-years, an absolute magnitude of 0.6 and an apparent magnitude of 0 (by definition). a) At peak brightness, how many times brighter will Betelgeuse be than Vega? b) Approximately what apparent magnitude does this correspond to? c) The Sun is about -26.5 apparent magnitude. What fraction of the Sun's brightness will Betelgeuse be?arrow_forwardThe Orion Nebula is about 20 light-years (20 × 1018 cm) across, enclosing a roughly spherical area with a volume of 4.19 × 1057 cm3. Calculate the number of 0.1 solar mass stars that might be formed in such a nebula. Assume that the nebula has a density of 1000 atoms/cm3.arrow_forward
- For the PP chain 0.7% of the mass participating in nuclear fusion is liberated as energy which produces a star's luminosity. Assume that the core of a main sequence star consists of 10% of its total mass. Hence, estimate the lifetime of a star on the main sequence in terms of its luminosity L/L. Give your answer in years. You may use the observed mass-luminosity relation L x M³.5, where M is the star's total mass. Using typical values, calculate estimates for the main sequence lifetime of a KO star and a 05 star. Describe briefly why your estimate might be more accurate for K stars compared to O stars.arrow_forwardA 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_forwardIn the H-R diagram we see that stellar masses__________ downward along the main sequence. At the upper end of the main sequence, the hot, luminous O stars can have masses as high as _________ or more times that of the Sun. On the lower end, cool, dim M stars may have as little as __________ times the mass of the Sun. Many more stars fall on the lower end of the main sequence than on the upper end, which tells us that _________stars are much more common than __________ stars.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_forwardYou can use the equation in Exercise 22.34 to estimate the approximate ages of the clusters in Figure 22.10, Figure 22.12, and Figure 22.13. Use the information in the figures to determine the luminosity of the most massive star still on the main sequence. Now use the data in Table 18.3 to estimate the mass of this star. Then calculate the age of the cluster. This method is similar to the procedure used by astronomers to obtain the ages of clusters, except that they use actual data and model calculations rather than simply making estimates from a drawing. How do your ages compare with the ages in the text? Figure 22.10 NGC 2264 HR Diagram. Compare this HR diagram to that in Figure 22.8; although the points scatter a bit more here, the theoretical and observational diagrams are remarkably, and satisfyingly, similar. Figure 22.12 Cluster M41. (a) Cluster M41 is older than NGC 2264 (see Figure 22.10) and contains several red giants. Some of its more massive stars are no longer close to the zero-age main sequence (red line). (b) This ground-based photograph shows the open cluster M41. Note that it contains several orange-color stars. These are stars that have exhausted hydrogen in their centers, and have swelled up to become red giants. (credit b: modification of work by NOAO/AURA/NSF) Figure 22.13 HR Diagram for an Older Cluster. We see the HR diagram for a hypothetical older cluster at an age of 4.24 billion years. Note that most of the stars on the upper part of the main sequence have turned off toward the red-giant region. And the most massive stars in the cluster have already died and are no longer on the diagram. Characteristics of Main-Sequence Starsarrow_forwardBefore the star that became SN 1987A exploded, it evolved from a red supergiant to a blue supergiant while remaining at the same luminosity. As a red supergiant, its surface temperature would have been approximately 4000 K, while as a blue supergiant, its surface temperature was 16,000 K. How much did the radius change as it evolved from a red to a blue supergiant?arrow_forward
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