Laboratories and Webpage designed by Andrew Nicholson 2004

Introduction:

In this lab we will be measuring the rate of rotation of different clouds of hydrogen surrounding stars, called nebula.  We will measure the rate of rotation of a nebula of ionized hydrogen surrounded by very hot stars.  The rotation can be measured from the frequency Doppler Shift of the hydrogen intensity in the nebula. Now we will discuss some of the terms above.  Intensity is the average energy per unit area per unit time.  As a star radiates light, the light gets spread apart more and more the further the observer is from the star.  Intensity is just the measure of how much light there is in a certain area over some time.  Smiley is a radio telescope so it detects radio waves, not optical waves that our eyes detect.  Radio waves and optical waves are both electromagnetic waves, just radio waves have a much smaller frequency than optical waves.  Frequency is just the measure of the number of waves per unit time. 

Now let us discuss HII regions.  Many spiral galaxies contain stars surrounded by clouds of hydrogen.  The hydrogen closest to the star is heated to or above 10¹⁴ Kelvin or 1.8*10¹⁵ degrees fahrenheit.  Hydrogen atoms become unstable at these temperatures leading to the breakdown of the atom into a proton and an electron.  Hydrogen in this state is said to be ionized and we call this a HII region.  The free protons and electrons formed by the ionization of hydrogen can recombine forming another hydrogen atom.  At the time of formation the electron of the newly created hydrogen atom occupies a high energy level, but over time the electron will drop to a low energy level.  The transition in energy levels produces a photon, or a particle of light.  The photon produced by the recombining of the hydrogen atom then may travel outward to the next part of the hydrogen cloud, the HI region.  A HI region is neutral hydrogen.  The HI region surrounds the HII region and is below 10¹⁴ Kelvin so the hydrogen atoms are not unstable.  If the photon created in the HII region strikes an atom of neutral hydrogen in the HI region it can cause the electron of the neutral hydrogen to spin-flip. Think of a spin-flip as a change in the orientation of the electron. The spin-flip is unstable and eventually the electron flips back to its original form, creating another photon. For further discussion on spin-flip transitions see Lab 1.  These are the photons we detect with Smiley.  These photons have a wavelength of about 21 cm or a frequency of about 1.42 GHz. Thus we can study an HII region by detecting signals from the surrounding HI region. 

Because many nebulae surrounding stars are rotating, light coming from these regions experience a dopplar shift, or a shift in frequency. For more information on the Doppler effect see Lab 3.  As the nebula rotates some of the ihydrogen gas is traveling towards us and some of the it is moving away from us.  The radio waves given off by the hydrogen gas will be blue shifted at the part of the nebula moving toward us and will be red shifted at the part of the nebula moving away from us.  Because we know the base frequency of these waves, 1.42 GHz, and we know what the shifted frequency of the waves is we can calculate the rate of rotation of the source.  The Doppler shift is given by the equation:

where is the amount the frequency is shifted, is the base frequency (1.42 GHz), v is the velocity of the source, and c is the speed of light. So by solving for velocity we find that:

Now that we have found the different velocities of different regions coming toward and away from us, we can subtract these two velocities and find the rate of rotation of the nebula.

Procedure:

1. Please refer to the Smiley Users Manual for a complete explanation of how to get into Smiley as well as an explanation of Smiley's controls.
2. Here is a table of many different nebulea. Note the season and the time of day, will all of these nebulae be in the sky?

Right Ascension Values for the Seasons

Nebulae

3. Pick 2 of the above nebula.
4. Log into Smiley and enter the coordinates of one of the regions in NEW coordinates and click GO. (http://smiley.pari.edu:8080/smiley/login.html)
5. Check the CURRENT Coordinates with the NEW Coordinates.  Are they close? They should be, but we can get them even closer by using HandPaddle.  Do not worry about getting Smiley exactly on the NEW Coordinates, just get as close as you can. While using HandPaddle I found it easier to refer to the ALT and AZ instead of RA and DEC.
6. Now click on the Spectrum button.
7. Please set your IF GAIN to around 19. Some sources will require more IF GAIN than others; generally you want your IF GAIN as high as possible without losing data.
8. Right click on the graph and click on Show Grid.
9. Now click on Begin Scan.  You should see red dots appear on the graph to your right.
10. After the data points have reached the end of the graph, Smiley will start over again. You only need one set of points so click on Stop Scan when the data points start to repeat.
11. Now you need to save your scan, so click on Save Scan.
12. Click on Open Data File and open the scan you just saved.
13. Click on the List to bring up your data points.
14. Notice how the data points start with a Frequency Offset of -600 kHz, then go to 600 kHz, and finally the cycle begins again.  You only want the first cycle.
15. Starting from your intensity at 600 kHz highlight your data up to -600 kHz and copy this data.  Paste this data into a spreadsheet program, Excel is recommended. Be sure to leave 5 extra rows at the top.
16. Now go back to the Control Room and copy and paste the information at the top of the list (this includes the name of the file, the date, the time, the values of RA and DEC, and the IF GAIN) in the 5 extra rows you left above your data in the spreadsheet.
17. Your data may not be aligned, so align it by copying and pasting and increase or decrease the column width as you desire.
18. If you are using Excel, highlight both data columns. On the tool bar click on Insert, then Chart.
19. Now choose XY (Scatter) and Scatter with data points connected by lines without markers.  Click on Next.
20. Make sure your graph looks something like the graph below and click Next.

21. Now label your axes. Your x-axis should be frequency while your y-axis should be Intensity.  Also label your graph.  Now click Finish.
22. Pick two points on your graph. If there is only one peak then pick points at the bottom of the peak.  If there is more than one peak then pick the points at the top of the two peaks.  To find the value of the frequency simply click on the point that corresponds with the peak or look at the data recorded from Smiley.  Some examples of points chosen are below.

23. From these frequencies we want to calculate the rate of rotation of the nebulae. Each frequency will tell us the velocity of one area of the nebula, but by subtracting the two velocities from each other we can get an idea about how quickly the nebula is rotating.  Calculate the rate of rotation of your nebula.  Some sample calculations can be found below.
24. Repeat steps 4-23 for your other nebula.

Challenge Question: What are the rates of rotation in miles per hour?