WK11_Dark_Matter
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School
Indiana University, Bloomington *
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Course
A105
Subject
Astronomy
Date
Dec 6, 2023
Type
docx
Pages
4
Uploaded by DrIron12403
A105 – Stars & Galaxies
Name:
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Week 11 Exploration
Dark Matter in the Milky Way
Learning Goals
– Students should be able to:
use models of galaxy rotation to determine the mass of the Milky Way.
estimate the relative amounts of ordinary matter and dark matter in our galaxy.
explain one line of evidence that led to the discovery of dark matter.
Background
The measurement of the rotation speeds of spiral galaxies was among the first evidence for the
existence of dark matter in our universe.
The banner image on Canvas page is an example of how
galaxy rotation is measured.
The panel on the left is an image of a galaxy. On the right, different
parts of this galaxy have been colored to tell us if the stars in that part of the galaxy are moving
towards us (blue), or away (red), or have no motion either towards or away (green). The darker the
shade of blue or red, the faster the motion. To get this information astronomers use spectra of
galaxies and the so called Doppler shift.
This method was pioneered in the 1970s by the astronomer Vera Rubin to measure the rotation of
many galaxies. In particular, for each galaxy she measured the rotation speed starting from the
center, then moving towards the edges (let’s say she picked only the receding (red) or the
approaching (blue) side - it does not matter). From these rotation speeds, astronomers can
calculate the mass of a galaxy using the law of gravity.
Rubin found that the rotation speeds of
galaxies were faster on the edges than could be explained by the amount of visible matter (stars
and gas), in the galaxies she studied.
So based on this one may conclude that other galaxies appear to have dark matter, but what about
ours? Getting the rotation speeds of other galaxies is easier than of our own galaxy (since we are
inside), but in decades since Rubin’s work astronomers found ways to measure it.
What to do and how
In this week's exploration, we'll use measurements of rotation speed to estimate the percentage of
the mass of the Milky Way that is the dark matter. Our measurements are given as
rotation speeds
at nine distances from the center of the Milky Way
. They are given in this table:
Distance
from the
center
(thousand
s of LY)
Rotation
speed
(km/s)
10
215
1
15
219
27
224
33
224
40
225
50
225
65
220
80
215
100
211
To aid us in the estimate of the dark matter content we will use a method often employed in
science: comparison of actual measurements (the table) with
model calculations
.
“Plot” the measurements (place red dots) on the chart below. The chart has various curves that
correspond to various model calculations. The models are calculated with different fractions of
dark matter, from no dark matter (the bottom model) to 86% dark matter (the top model).
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Then answer the following questions:
1.
Based on our galaxy’s rotation curve, what
percentage of the matter in the Milky Way
is dark matter? (Do not consult other
sources of information)
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2.
The Sun is located about 26,000 light years
from the center of the Milky Way. Based on
the rotation data, what should the velocity
of the Sun be as it orbits the Milky Way?
(Do not consult other sources of
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information)
3.
How fast (in km/s) would the Sun orbit
around the center of the Milky Way if our
galaxy contained NO dark matter? Give
number
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4.
Explain why studies of galaxy rotation use
spiral galaxies that are oriented so that we
see them “edge-on” (sideways) rather than
“face-on” (so that they look like a circle)?
Hint: Rotation velocity is measured using
the Doppler shift which arises only from a
velocity towards or away from us.
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5.
[extra credit] Explain why elliptical galaxies
cannot be used to measure the rotation.
6.
In your own words, explain why the
observed Milky Way rotation curve (the
rotational velocity vs. distance curve)
provides evidence for dark matter in the
Milky Way.
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