Interpretation of the Recorded Data

Joachim Köppen Strasbourg 2010

Format of the Data

The record file is a plain text file, and its contents may look like this (from a manual observation):
18:47:48 313.6 46.6 0 0 6.26 1420.16 0.00781250 1 64 3.3 3.8 6.8 15.8 ...
18:47:49 313.3 46.8 0 0 6.48 1420.16 0.00781250 1 64 3.2 4.5 6.5 13.3 ...
* G90 18:47:50 313.6 46.6 0 0 6.26 1420.16 0.00781250 1 64 3.7 4.0 7.0 12.5 ...
18:47:51 316.0 24.9 0 0 -7.29 1420.16 0.00781250 1 64 5.7 4.3 6.7 14.6 ...
18:47:52 316.0 24.9 0 0 -7.29 1420.16 0.00781250 1 64 6.9 4.3 8.1 15.8 ...
... and so on ...

The first line gives the geographical coordinates of the telescope, the next two lines are the spectra taken at the current position; then follows the user's command go to the next source G90 which is the Galactic Plene at longitude 90. The following lines are the spectra taken there ... except for the line right after the command, since it took some time for the telescope to move to the new position. For the sake of legibility of the Web pages, we have cut the line lengths, as indicated by the dots ...

The results of observations in batch mode could look like this:
* cmdfil: line 6 : record
23:40:30 147.0 39.3 0 0 2.82 1419.43 0.00781250 6 248 5.0 6.0 11.0 21.0 42.0 ...
* cmdfil: line 7 : pointcorr -0.5 -3.5
* cmdfil: line 9 : galactic 220 0
23:41:20 145.5 25.9 0 0 2.28 1419.43 0.00781250 6 248 2.0 3.0 4.0 8.0 16.0 29.0 ...
* cmdfil: line 10 :360
23:41:36 145.7 26.1 0 0 2.35 1419.43 0.00781250 6 248 2.0 3.0 5.0 9.0 17.0 30.0 ...
23:41:49 145.7 26.1 0 0 2.33 1419.43 0.00781250 6 248 2.0 3.0 4.0 9.0 17.0 30.0 ...
.... and so on

Here, the lines with * cmdfil: line simply record the commands from the batchfile, so that we can recognize more easily what the data refers to. Also, in case of problems, the error messages will be recorded.
In the above example, we see that the recording was switched on, one spectrum follows, then the values for the pointing correction were accepted, then came the command to goto the position with galactic longitude 220 and latitude 0, one more spectrum follows, and then came the request to stay at that position for 300 seconds. The following spectra thus are the relevant observational data ...

The spectral data taken at each instant of time are recorded as a new line in the file. The data are separated by blank spaces, the fields have this meaning:

A first look

Being in the form of a text file, the data can easily be imported into any suitable program for data analysis, including a spread sheet program, such as MS Excel. In the following, we use this program. Importing is done by: File > Import > Text File > select your Text File > Delimited Text File > Delimiter is Spaces > Finish.

Now, each row (or line) represents a single spectrum taken at the time instant as indicated by the column at left. The columns give the data as described above. It is helpful to insert a row above the first spectrum, and type in what each column means.

If you deal with a file which recorded data taken at several different sources, it is best to separate the data array of each source into its own worksheet.

Let us deal with a worksheet containing the spectra for a certain source. We shall suppose that we had recorded several of many spectra for this source using the same frequency grid. Before starting the analysis, it is best to have a first look at the data.

First, we should like to see what the overall average spectrum looks like. To do this, we have to make rows that contain the abscissae and the ordinates for this plot:

Now select these two arrays and insert a Scatter Plot, which could look like this
From this plot we may see that there is a clear spectral feature centered on about 1420.25 MHz, and that the background is at a level of about 500 counts. The feature - it is from the Galactic Plane - is only 30 counts above the background, and it extends from 1420.10 to 1420.32 MHz. If we had been present during the observation, we would have seen this plot as the result of the time-averaged spectrum, something like this:
There is another helpful first plot, especially during the time when we had strong and time-variable interference. This is to inspect the frequency-averaged flux as a function of time. For this purpose we put into one column to the right of the block of data the averages of the fluxes, for each time instant. Since the first 8 and the last 8 points of a spectrum do not represent the full value of the flux, we extend the averaging only to the inner part of the spectrum. In the case of our example data, this covers the columns S to BN. The plot of this new column against time (in column A) looks like this:
This graph showed us that the level of the average flux has been quite stable in the first 6 minutes, but that after about 16:30 there had been strong fluctuations, especially the deep drops down to 200 counts. This indicated the presence of short but strong interference. However, at present, we no longer have any such problems.

The Waterfall plot A good way to look at the data and judge its quality is the 'waterfall' map, which shows the fluxes in a false-colour map as a function of both frequency and time. This map is done in real-time by the telescope software, but it can also be constructed afterwards from the recorded data. In Excel we have to use a few small tricks:

This map shows that the flux is greatest near the centre of the spectral range (frequency no.31) and that for instance, just before time no.151 the fluxes dropped sharply, as we had seen in the drop of frequency-averaged flux at 16:30.

The map below shows the waterfall diagram of an in-band interference, consisting of two signals. To bring out the details of the signals, we had subtracted from each spectrum the background determined for that instant, and also show only some part of the entire spectrum:

One notes that the left-hand signal is concentrated on a number of discrete frequencies. This identifies the signal as human-made, because radio emission from celestial sources does not exhibit such narrow structures. The speeds of the motions of hydrogen clouds are high enough to smear out any structure as fine as that.

Subtraction of the Baseline Since the radio signal from the celestial sources are rather weak, the spectrum shows always some background signal, mainly from the noise generated by the receiver itself. There may also be continuum radio emission from the sky, and unfortunately also noise from the ever-growing electronic pollution by various electronic equipment, such as computers and their switched power supplies. This essentially frequency-independent noise power simply adds up to the received signals at all frequencies. Therefore we may deal with it by simply subtracting this background, or the baseline as it is called in radio spectroscopy.

If the baseline is constant in frequency, it suffices to determine its level by measuring it left and right of the spectral feature of the source, and subtract the average value from the data. Let us do this for our above example. First, we apply this to the time-averaged spectrum:

A convenient way is do this manually, by plotting the baseline-subtracted spectrum and adjusting the baseline guess value until the fluxes in the presumed empty regions on both sides of the spectral feature are reduced to zero. The blue curve shows the result obtained with a constant baseline. However, it is evident that this is not able to match the background on both sides of the feature. If one notices that the background is not constant, one would resort to assuming that it could be approximated by a sloping straight baseline. As shown in the example, one adjusts the two guess values corresponding to the two ends of the spectrum. This gives a much more satisfactory match of the data. We note that the background on the low-frequency side may not be well determined, because one does not have much of a horizontal part.

In this way, one obtains the true spectrum of the source. Integration over all frequencies then gives the emission from the source.

Reduction to radial velocity For galactic and extra-galactic sources, the frequency is not the physically relevant of interessant quantity. It rather is the radial velocity. This is obtained from comparing the frequency to that of the natural frequency of the hydrogen line, namely f0 = 1420.406 MHz:

Vrad = - c * (f - f0) / f0 - VLSR
Since the Earth is moving around the Sun with 30 km/s, and the telescope moves due to the Earth's rotation, we correct the apparent radial velocity to the reference of the Local Standard of Rest. To show the spectrum with respect to this abscissa, one inserts another row below the row of the frequencies, and fills it with the array of radial velocities corresponding to each frequency. The resultant plot looks like this:
It shows that at the is galactic position, the hydrogen gas moves away from us - more precisely from the LSR - with about 10 km/s on the average, and that the radial velocities of the individual clouds seen along the line-of-sight are distributed over a range of +/-20 km/s.

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last update: Apr. 2010 J.Köppen