Dark Matter Teacher Guide - Perimeter Institute

Supplementary Information
Physicists use a similar equation to find the speeds of
stars within galaxies, but there are two differences. First,
physicists do not directly measure the frequency shift of
light waves emitted by a star. Instead, they measure the
frequency shift of radio waves emitted by hydrogen gas
orbiting at the same speed as the star. This allows them to
calculate the speed of the gas and thus the speed of
the star.
The second difference is that physicists use a slightly
different equation from Equation 3.1 because
electromagnetic radiation travels at the speed of light and
must be handled using Einstein’s theory of relativity, as
detailed in Appendix D on the DVD-ROM.
Note that in the animation of Doppler shifted stars in
the video we have greatly exaggerated the colour changes
associated with the Doppler effect in order to
highlight them.
Doppler Effect and Orientations of Galaxies
It is important to note that the Doppler effect only
measures the speed of a star towards or away from us. It
does not measure any sideways or transverse motion with
respect to Earth.
If a galaxy is oriented so that we can only see the edge
of its orbital plane (an edge-on galaxy) some of its stars are
moving directly towards us and some are moving directly
away from us, as in Figure 11. We can measure the orbital
speeds of these stars using the Doppler effect.
However, if a galaxy’s orbital plane faces Earth directly
(a face-on galaxy) then all of its stars move with purely
transverse velocities relative to Earth, as in Figure 12.
In this case, both the stars and hydrogen gas do not exhibit
any frequency shift and we cannot measure their speeds
using the Doppler effect. Only a small fraction of galaxies
are face-on.
Most galaxies lie somewhere in between the two extremes
of being face-on or edge-on. They have orbital planes
tilted at some angle towards us. So, physicists can use the
Doppler effect to measure a component of the velocities
of their stars. Physicists then find the total velocities by
determining the angle of the tilt and adjusting the measured
Doppler speeds accordingly.
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Where did the data for Triangulum come from?
The speed (v = 123 km/s) and radius (r = 4.0 ×10 20 m)
values for Triangulum used in the video came from recent
measurements of this galaxy. The complete set of data is in
the Appendix in Section F.
Measuring the Orbital Radius of a Star
Another question that arises from this chapter of the video
is how physicists measure the radius of the orbit of a star
in a distant galaxy. Appendix E on the DVD-ROM answers
this question.
Figure 11 Edge-on galaxy
Figure 12 Face-on galaxy. For an edge-on galaxy, we can measure the
orbital speeds of stars via the Doppler effect. For a face-on galaxy, we
cannot.