Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Question
Chapter 23, Problem 21Q
To determine
(a)
The distance that a single maser moves during a 4-month period.
To determine
(b)
The distance to the galaxy.
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Using our example from the previous unit, let's try to determine the Hubble time for this example universe. You were given that a good representative galaxy receded at a speed of 4000 km/s and was found to be 20 Mpc away. With that in mind, what would the age of that universe be in years (aka what is that universe's Hubble time)? Go ahead and take the number of kilometers per Mpc to be approximately 3.1*10^19 km/Mpc. While this problem may look scary at first, this is really just bringing you full circle to one of the unit conversion problems you encountered at the beginning of this course.
The Tully-Fischer method relies on being able to relate the mass of a galaxy to its rotation velocity.
Stars in the outer-most regions of the Milky Way galaxy, located at a distance of 50 kpc from the
galactic centre, are observed to orbit at a speed vrot
determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of
the Solar mass.
250 km s-1. Using Kepler's 3rd Law,
Another commonly calculated velocity in galactic dynamics is the escape velocity vesc, that is
the minimum velocity a star must have in order to escape the gravitational field of the galaxy.
(a) Starting from the work required to move a body over a distance dr against f show that
the escape velocity from a point mass galaxy is vse = 2GM/r where r is your initial distance.
(b) Since we know galaxies aren't actually point-masses, also show that vesc from r for a
galaxy with a p(r) x r-² density profile is vse = 2v²(1+ ln(R/r)). Here you must assume
that R is a cutoff radius at which the mass density is zero.
(c) The largest velocity measured for any star in the solar neighbourhood, at r=8 kpc,
is 440 km/s. Assuming that this star is still bound to the galaxy, find the lower limit (in
kiloparsecs), to the cutoff radius R and a lower limit (in solar units) to the mass of the
galaxy. Note the solar rotation velocity is 220 km/s.
Chapter 23 Solutions
Universe: Stars And Galaxies
Ch. 23 - Prob. 1QCh. 23 - Prob. 2QCh. 23 - Prob. 3QCh. 23 - Prob. 4QCh. 23 - Prob. 5QCh. 23 - Prob. 6QCh. 23 - Prob. 7QCh. 23 - Prob. 8QCh. 23 - Prob. 9QCh. 23 - Prob. 10Q
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- If a galaxy is 8.9 Mpc away from Earth and recedes at 497 km/s, what is H. (in km/s/Mpc)? km/s/Mрс What is the Hubble time (in yr)? years How old (in yr) would the universe be, assuming space-time is flat and the expansion of the universe has not been accelerating? years How would acceleration change your answer? If the expansion of the Universe has been accelerating, the Universe could be substantially younger than the value entered above. If the expansion of the Universe has been accelerating, the Universe could be substantially older than the value entered above.arrow_forward(e) An optical spectrum of a galaxy has a magnesium absorption line at a wavelength of 531.3 nm. Given that the rest wavelength of the calcium line is 517.5 nm, what is the redshift of this galaxy? -1 -1 Assuming a value for Hubble's Constant (Ho) of 67.6 km s-¹ Mpc-¹, estimate the distance to the galaxy in Megaparsecs. Note any assumptions you have made.arrow_forwardAnother commonly calculated velocity in galactic dynamics is the escape velocity vesc, that is the minimum velocity a star must have in order to escape the gravitational field of the galaxy. (a) Starting from the work required to move a body over a distance dr against f show that the escape velocity from a point mass galaxy is vsc = 2GM/r where r is your initial distance. (b) Since we know galaxies aren't actually point-masses, also show that vesc from r for a galaxy with a p(r) xr¯² density profile is vese that R is a cutoff radius at which the mass density is zero. = 2v(1+ ln(R/r)). Here you must assume (c) The largest velocity measured for any star in the solar neighbourhood, at r=8 kpc, is 440 km/s. Assuming that this star is still bound to the galaxy, find the lower limit (in kiloparsecs), to the cutoff radius R and a lower limit (in solar units) to the mass of the galaxy. Note the solar rotation velocity is 220 km/s.arrow_forward
- If a galaxy is 9.0 Mpc away from Earth and recedes at 488 km/s, what is H, (in km/s/Mpc)? | km/s/Mpc What is the Hubble time (in yr)? | years How old (in yr) would the universe be, assuming space-time is flat and the expansion of the universe has not been accelerating? years How would acceleration change your answer? O If the expansion of the Universe has been accelerating, the Universe could be substantially younger than the value entered above. O If the expansion of the Universe has been accelerating, the Universe could be substantially older than the value entered above. Need Help? Read Itarrow_forwardIf the diameter of the Milky Way Galaxys visible disk, 80,000 ly, is represented in a model by a dinner plate with a diameter of 10 inches, what is the model distance to galaxy M31, 2.6 millionly away? What is the model distance to the Virgo galaxy cluster, 16 Mpc away? (Convert answers to feet.)arrow_forwardStars form in the Milky Way at a rate of about 1 solar mass per year. At this rate, how long would it take for all the interstellar gas in the Milky Way to be turned into stars if there were no fresh gas coming in from outside? How does this compare to the estimated age of the universe, 14 billion years? What do you conclude from this?arrow_forward
- Based on your analysis of galaxies in Table 26.1, is there a correlation between the population of stars and the quantity of gas or dust? Explain why this might be.arrow_forwardAssume that dark matter is uniformly distributed throughout the Milky Way, not just in the outer halo but also throughout the bulge and in the disk, where the solar system lives. How much dark matter would you expect there to be inside the solar system? Would you expect that to be easily detectable? Hint: For the radius of the Milky Way’s dark matter halo, use R=300,000 light-years; for the solar system’s radius, use 100 AU; and start by calculating the ratio of the two volumes.arrow_forwardThe first clue that the Galaxy contains a lot of dark matter was the observation that the orbital velocities of stars did not decreases with increasing distance from the center of the Galaxy. Construct a rotation curve for the solar system by using the orbital velocities of the planets, which can be found in Appendix F. How does this curve differ from the rotation curve for the Galaxy? What does it tell you about where most of the mass in the solar system is concentrated?arrow_forward
- Can an elliptical galaxy evolve into a spiral? Explain your answer. Can a spiral turn into an elliptical? How?arrow_forwardSuppose the Sun orbited a little farther out, but the mass of the Galaxy inside its orbit remained the same as we calculated in Exercise 25.19. What would be its period at a distance of 30,000 light-years?arrow_forwardOnce again in this chapter, we see the use of Kepler’s third law to estimate the mass of supermassive black holes. In the case of NGC 4261, this chapter supplied the result of the calculation of the mass of the black hole in NGC 4261. In order to get this answer, astronomers had to measure the velocity of particles in the ring of dust and gas that surrounds the black hole. How high were these velocities? Turn Kepler’s third law around and use the information given in this chapter about the galaxy NGC 4261-the mass of the black hole at its center and the diameter of the surrounding ring of dust and gas-to calculate how long it would take a dust particle in the ring to complete a single orbit around the black hole. Assume that the only force acting on the dust particle is the gravitational force exerted by the black hole. Calculate the velocity of the dust particle in km/s.arrow_forward
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