UNDERSTANDING THE UNIVERSE(LL)-W/CODE
3rd Edition
ISBN: 9780393869903
Author: PALEN
Publisher: NORTON
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Question
Chapter 14, Problem 34QAP
To determine
Evidences for a supermassive black hole at the centre of the Milky Way; Comparison of mass of supermassive black holes at the centre of our galaxy to the ones found in most other spiral galaxies.
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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…
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.
Which of the following best describe the reasons we have to infer that a supermassive blackhole lurks in the centre of our galaxy?
Stars keep disappearing from view as they get swallowed up in the galactic centre.
Tight orbit of stars around an invisible companion & giant bubbles of cold, star forming gas have been expelled from galactic centre.
We can measure the gravitational waves coming from such an enormous black hole.
O Tight orbit of stars around an invisible companion & giant bubbles filled with gamma rays expelled from the galactic centre.
Chapter 14 Solutions
UNDERSTANDING THE UNIVERSE(LL)-W/CODE
Ch. 14.1 - Prob. 14.1CYUCh. 14.2 - Prob. 14.2CYUCh. 14.3 - Prob. 14.3CYUCh. 14.4 - Prob. 14.4CYUCh. 14 - Prob. 1QAPCh. 14 - Prob. 2QAPCh. 14 - Prob. 3QAPCh. 14 - Prob. 4QAPCh. 14 - Prob. 5QAPCh. 14 - Prob. 6QAP
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- Suppose somebody proposed that rather than invoking dark matter to explain the increased orbital velocities of stars beyond the Sun’s orbit, the problem could be solved by assuming that the Milky Way’s central black hole was much more massive. Does simply increasing the assumed mass of the Milky Way’s central supermassive black hole correctly resolve the issue of unexpectedly high orbital velocities in the Galaxy? Why or why not?arrow_forwardThe globular clusters revolve around the Galaxy in highly elliptical orbits. Where would you expect the clusters to spend most of their time? (Think of Kepler’s laws.) At any given time, would you expect most globular clusters to be moving at high or low speeds with respect to the center of the Galaxy? Why?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
- The best evidence for a black hole at the center of the Galaxy also comes from the application of Kepler’s third law. Suppose a star at a distance of 20 light-hours from the center of the Galaxy has an orbital speed of 6200 km/s. How much mass must be located inside its orbit?arrow_forwardSuppose the stars in an elliptical galaxy all formed within a few million years shortly after the universe began. Suppose these stars have a range of masses, just as the stars in our own galaxy do. How would the color of the elliptical change over the next several billion years? How would its luminosity change? Why?arrow_forwardWhat are the two best ways to measure the distance to a nearby spiral galaxy, and how would it be measured?arrow_forward
- When comparing two isolated spiral galaxies that have the same apparent brightness, but rotate at different rates, what can you say about their relative luminosity?arrow_forwardSuppose you have obtained spectra of several galaxies and have measured the observed wavelength of the H-Alpha line (rest wavelength = 656.3 nm) to be Galaxy 1: 658.1 nm. Galaxy 2: 667.1 nm. Galaxy 3: 677.6 nm. Calculate the radial velocity of each of these galaxies.arrow_forwardYou observe the H-alpha line of Hydrogen in a distant galaxy to have a wavelength of 754.4 nm. What is the radial velocity of the galaxy? Hint: The rest wavelength of H-alpha is 656 nm. I have to use the forumla mentioned in the photo I shared with this post.arrow_forward
- Observations of the central region of the galaxy M87 indicate that stars which are 60 light years later from the centre are orbiting the central supermassive black hole at speeds of 730kms^-1. Estimate the lads of the black hole, in solar masses.(You can assume circular motion, e.g. if you get 3 solar masses, type in 3). just wondering what formula I use?arrow_forwardIf the active core of a galaxy contains a black hole of 106 M, what will the orbital period be for matter orbiting the black hole at a distance of 0.23 AU? Hint: Use the formula for circular velocity, V. GM V hrarrow_forwardThe figure below shows the spectra of two galaxies A and B. Please can i get help with this questions below: 1. Which of these galaxies has ongoing star formation? How can you tell?2. One of these galaxies has Hubble type E3 while the other is SBb. Which is which? What does the 3 inE3 tell you about the galaxy? What does the SB in SBb tell you about the galaxy?3. What effects would dust have on the two spectra?4. Which galaxy would you expect to have more far-infrared emission? Explarrow_forward
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