Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 22, Problem 4Q
To determine
To explain:
The RR Lyrae stars. The way, RR Lyrae stars are useful to determine the distance from the Solar system to the center of the galaxy.
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A galaxy's rotation curve is a measure of the orbital speed of stars as a function of distance
from the galaxy's centre. The fact that rotation curves are primarily flat at large galactocen-
tric distances (vrot(r) ~ constant) is the most common example of why astronomer's believe
dark matter exists. Let's work out why!
Assuming that each star in a given galaxy has a circular orbit, we know that the accelera-
tion due to gravity felt by each star is due to the mass enclosed within its orbital radius r and
equal to v?/r. Here, ve is the circular orbit velocity of the star. (a) Show that the expected
relationship between ve and r due to the stellar halo (p(r) xr-3.5) does not produce a flat
rotation curve. (b) Show that a p(r) ∞ r¯² density profile successfully produces a flat ro-
tation curve and must therefore be the general profile that dark matter follows in our galaxy.
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 = 250 km s−1. Using Kepler’s 3rd Law, determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of the Solar mass.
Figure 2 shows the "rotation curve" of
NGC 2742. It plots the “radial velocity
(V)" (how fast material is moving
either toward or away from us) that is
measured for objects at different
distances (R = radius") from the
center of the galaxy. The center of the
galaxy is at 0 kpc (kiloparsecs) with a
speed of 9 km/sec away from us.
(These velocities have been corrected
for the observed tilt of the galaxy and
represent true orbital velocities of the
stars and gas.)
200
100
U4779
-100
As you can see, one side of the galaxy
is moving with a negative velocity
(spinning toward us), while the other
side has a positive velocity (spinning
away from us). Using Newton's
gravity equation, we will be able to
determine the gravitational mass of the
entire galaxy and how the mass varies
versus distance from the galaxy's center.
-200
-8
8
-4
Radius (kpc)
Read the following text carefully and follow the instructions:
Select five radii spaced evenly from 0-10 kpc across the galaxy. Your selections should…
Chapter 22 Solutions
Universe: Stars And Galaxies
Ch. 22 - Prob. 1QCh. 22 - Prob. 2QCh. 22 - Prob. 3QCh. 22 - Prob. 4QCh. 22 - Prob. 5QCh. 22 - Prob. 6QCh. 22 - Prob. 7QCh. 22 - Prob. 8QCh. 22 - Prob. 9QCh. 22 - Prob. 10Q
Ch. 22 - Prob. 11QCh. 22 - Prob. 12QCh. 22 - Prob. 13QCh. 22 - Prob. 14QCh. 22 - Prob. 15QCh. 22 - Prob. 16QCh. 22 - Prob. 17QCh. 22 - Prob. 18QCh. 22 - Prob. 19QCh. 22 - Prob. 20QCh. 22 - Prob. 21QCh. 22 - Prob. 22QCh. 22 - Prob. 23QCh. 22 - Prob. 24QCh. 22 - Prob. 25QCh. 22 - Prob. 26QCh. 22 - Prob. 27QCh. 22 - Prob. 28QCh. 22 - Prob. 29QCh. 22 - Prob. 30QCh. 22 - Prob. 31QCh. 22 - Prob. 32QCh. 22 - Prob. 33QCh. 22 - Prob. 34QCh. 22 - Prob. 35QCh. 22 - Prob. 36QCh. 22 - Prob. 37QCh. 22 - Prob. 38QCh. 22 - Prob. 39QCh. 22 - Prob. 40QCh. 22 - Prob. 41QCh. 22 - Prob. 42QCh. 22 - Prob. 43QCh. 22 - Prob. 44QCh. 22 - Prob. 45QCh. 22 - Prob. 46QCh. 22 - Prob. 47QCh. 22 - Prob. 48QCh. 22 - Prob. 49QCh. 22 - Prob. 50Q
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