The following section provides an overview of various activities that can be completed by students while observing pulsars. Each section provides an explanation of what can be done as well as some examples where relavent.
Parkes Data Files
The data that arrives from the Parkes telescope contains 8 frequency channels, which displays an intensity that was recorded over time and averaged over the pulse period. Although the most basic characteristic of the pulsar signal is the pulse periodicity, another distinguishable feature is the Dispersion Measure (DM). As radio waves travel through the interstellar medium, they encounter ionised gas with a refractive index different to that of empty space. This ionised gas has the effect of putting a delay in the arrival time of the radio pulse, depending on the frequency of the radiation. The higher frequencies end up traveling faster through the interstellar medium, so we see pulses in the highest frequency arriving first. Each lower frequency channel exhibits a pulse that arrives slightly after the one before it, all the way down to the lowest frequency. The first column in the data file is the time that the measurement was taken. All the other columns display the other frequency channels in order of highest to lowest.
Displaying Your Data File
The easiest way to see what the numbers in your Parkes Data File really means is to graph it. In this case we want a graph with time on the x (bottom) axis, and intensity on the y (vertical) axis. We also want a different set of coloured points for each frequency so we can tell the different times of arriving pulses. To produce a suitable graph in EXCEL, follow the following steps:
- First you need to import the text file on the web, in to an EXCEL spreadsheet. Download the file from the web and save it as a txt file on your computer.
- Open it in a text editor such as notepad. Choose from the edit menu --> select all --> copy.
- In a new excel document go to the edit menu and select --> paste special. An option box will come up, from which you want to paste the data into columns, seperated by commas.
- Depending on the display settings of your excel sheet, some of the data may be rounded down to zero. To fix this, highlight all of the numerical cells and press the "add decimal place" button until the data is displayed correctly.
- To produce a graph, highlight all of the cells and choose from the options menu --> insert --> chart. You will need to ensure that the first column is used as the x axis data, and all the rest are ploted as seperate sets of data points. The output should look something like this:
Measuring the Dispersion Measure
The Dispersion Measure (DM) is a parameter that describes the electron content of the gas in between an observer and the pulsar. The time delay that is observed is given by:
where ν is the frequency in MHz, and t is time in seconds. This equation can be modeled as a straight line:
where y is the time the peak of the pulse arrives (t), x is frequency term (ν-2) and the gradient m = 4.15 × 103 × DM. Hence we can easily find the DM by ploting the peak arrival times as measured by our graph. You should find a straight line as follows:
From this line of best fit, we find the gradient m = 2.14 × 106. Hence we can rearrange the gradient to find the DM:
Note: the peaks might not allways be clearly visable above the noise. In the graph bellow you can see an example where the data for the peaks falls bellow the noise level. The easiest way to fix this is to split the data in to less frequency channels.
Measuring the Distance to a Pulsar
When trying to find a meaningful relation for the distribution of pulsars over the galactic disk, it is necessary to know the distance to a detected pulsar. The Dispersion Measure provides a very easy way for working out distances to pulsars. We know that the pulses of a pulsar accross all frequencies depart the pulsar at the same time, but subsequently spread out due to their varying speeds for travelling through the interstellar meddium. The dispersion effect is proportional to the density of electrons along the line of sight. We can find the distance to a pulsar using the following formula:
where ne is the density of electrons in the glactic disk, which is known to be approximately 0.03 cm-3.