An SRT Activity:
Measuring the Doppler
Shift of Galactic Hydrogen
If
you have not used the SRT before, it is strongly recommended that you complete
the data reduction exercise prior to performing this activity.
Objective:
The
21 cm line produced by neutral hydrogen in interstellar space provides radio
astronomers with a very useful probe for studying the speeds of interstellar
objects. By observing hydrogen lines at
different points along the galactic plane, one can show that the angular
velocity increases as you look at points closer to the galactic center. The purpose of this experiment is to create a
rotational curve for the Milky Way Galaxy using 21 cm spectral lines observed
with a small radio telescope (SRT). The
sample observations for this experiment will be made using the MIT Haystack
Observatory’s SRT. The rotational curve
will be created by plotting the maximum velocity observed along each line of
sight versus the distance of this point from the Galactic center.
Introduction: The 21 cm Line of
Neutral Hydrogen
Hydrogen
is the most abundant element in the cosmos; it makes up 80% of the universe’s
mass. Therefore, it is no surprise that
one of the most significant spectral lines in radio astronomy is the 21 cm
hydrogen line. In interstellar space, gas is extremely cold; hydrogen atoms in
the interstellar medium are at such low temperatures (~100 K) that they are in
the ground electronic state. This means
that the electron is as close to the nucleus as it can get, and it has the
lowest possible allowed energy. Radio
spectral lines arise from changes between one energy level to another.
A
neutral hydrogen atom consists of one proton and one electron in orbit around
the nucleus. Both the proton and the electron have their own internal spin, but
they do not spin in just one direction.
They can spin in the same direction (parallel) or in opposite directions
(anti-parallel). The energy carried by
the atom in the parallel spin is greater than the energy it has in the
anti-parallel spin. Therefore, when the
spin state flips from parallel to anti-parallel, energy (in the form of a low
energy photon) is emitted at a radio wavelength of 21 cm. This 21 cm radio spectral line corresponds to a
frequency of 1.420 GHz.
Observations
of the 21 cm line can be used to create the rotation curve for our Milky Way
Galaxy. If hydrogen atoms are
distributed uniformly throughout the Galaxy, a 21 cm line will be detected from
all points along the line of sight of our telescope. The only difference will be that all of these
spectra will have different Doppler shifts, since they are moving at different
velocities relative to the Earth. The distance to the Galactic center is known
to be 8.5 kpc, or 2.6 x 1017 km.
Procedure:
1)
Use
the SRT to observe the H-line spectrum at several points in the plane of the
galaxy. Choose galactic coordinates that
are currently visible. (You can visually
determine this by looking at the SRT software interface.) A sample command file is as follows:
|
:
freq 1420.4 4 |
/
set radiometer center frequency and observing mode 4 |
|
:
azel 180 45 |
/
point south at 45 degrees |
|
:
noisecal |
/
calibrate radiometer |
|
:
galactic 0 0 |
/
move telescope to Galactic center |
|
:
record g00.rad |
/
start data file |
|
:
180 |
/
take data for 600 seconds |
|
:
roff |
/
turn off data recording |
|
:
galactic 15 0 |
/
move telescope to Galactic longitude of 15 degrees |
|
:
record g15.rad |
|
|
:
180 |
|
|
:
roff |
|
|
:
galactic 30 0 |
/
move telescope to Galactic longitude of 30 degrees |
|
:
record g30.rad |
|
|
:
180 |
|
|
:
roff |
|
|
|
|
|
|
/
repeat for longitudes to 90 degrees |
This suggested observing schedule provides spectra
for 5 to 8 points in the galactic plane.
You should modify the number of points and the exact positions along the
galactic plane to accommodate which areas of the galactic center are currently
overhead. Taking data on either side of
the galactic plane may be especially helpful.
You may wish to coordinate your positions with other students to enable
a complete survey to be taken by the class as a whole.
2)
The
real time control program contains a routine that calculates the VLSR. You must copy this data point down yourself –
it is displayed in the lower right hand corner of the SRT software. This is the velocity of the local solar
region (our approximate speed relative to the galaxy).
3)
Use
the data reduction techniques you learned in previous exercises to plot a
spectrogram at each galactic coordinate where you took data. Note that the software plots this in real
time on the screen as well, you may wish to take notes while the SRT is
running!
4)
Note
that there are actually two peaks on your graphs. This is telling you something important about
the structure of our galaxy. In trying
to answer the question, “Why are there two peaks?”, think about the fact that
the SRT is picking up all signals along the line of sight.
5)
Determine
the frequencies of both hydrogen lines at each position using your data. You may wish to compare your spectra with a
textbook example taken with no Doppler shift.
Take note of which of the two frequencies had the greater relative
intensity.
6) Use the general Doppler
shift formula to derive the following formula.
Be sure to show your work!
The velocity V of a Doppler
shifted hydrogen frequency is:
Vc
= Velocity of light = 299,790 km/s
VLSR
= Velocity of observer relative to local standard of rest
f
= Peak frequency of hydrogen spectral line
7)
For
each of the frequencies determined in Question 4, determine the associated
Doppler shift velocity. You may wish to
create a new spreadsheet to perform the necessary calculations for you!
8)
Graph
these velocities as a function of position along the galactic axis.
9)
Is
the Doppler shift telling us about the actual velocity of hydrogen or only one
component? Comment on how this affects
your interpretation of the data.
10)
From
your graph, what can you determine about the structure of our galaxy? You may want to research what is known and
see if you results make sense in that context.