Summary In this Activity, we will examine: 1. Why radio astronomers use arrays of radio telescopes 2. Some fundamental principles of radio interferometry This image shows the radio emission at a wavelength of 13 cm from the planet Jupiter and from a disk of electrons which are trapped in Jupiter’s magnetic field. Radio images like this are made from observations taken using an array of radio telescopes. This image was obtained using the Australia Telescope Compact Array.
The angular resolution of a radio telescope measures its ability to discern fine detail in the structure of a radio source. For a single radio telescope the angular resolution can be written as: Resolution (R) (arcsec) = 2 x 10 5 x wavelength observed = / D telescope diameter The factor of 2 x10 5 is used to covert from radians to arcseconds. Remember: 1 degree = 3600 arcseconds 360 degrees = 2 radians Angular resolution of a single radio telescope
As an example, consider the angular resolution for the Effelsberg radio telescope. This is the second largest steerable radio telescope in the world, with a diameter of 100 m. At a wavelength of 6 cm the angular resolution is about 2 arcminutes (or 120 arcseconds). Optical telescopes can see much finer detail (typically about one arcsecond) than large radio telescopes like Effelsberg. The Effelsberg radio telescope has been in operation since It is used both as a single telescope and as part of a network of telescopes. This is because radio waves have such long wavelengths. To match the angular resolution of an optical telescope, a single radio telescope would have to have a diameter of many kilometres. Why?
Radio telescopes CAN achieve angular resolutions which are as good as, or even better, than those of optical telescopes. This is done using a technique called radio interferometry where the radio signals from two or more radio telescopes are combined. In most cases, a number of radio telescopes are linked together to form an array. Each telescope in an array can be considered to be a part of a much larger dish. To understand this better, lets start by considering a single-baseline interferometer, which is observing a distant point source. Radio Interferometry
A two-element interferometer wavefront Correlator B Bcos T2T1 Direction to source Computer disk P = The wavefront from a distant point source reaches the two telescopes T1 and T2. At each telescope the incoming radio waves are detected at the telescope focus and are converted into electrical signals. The signals from T1 and T2 are sent by a cable or optical fibre to a correlator where they are sampled and combined. Bsin
The radio wavefront reaches the telescope T1 first. It travels an extra path difference of P = B cos before it reaches telescope T2. The wavefront ‘sees’ a projected baseline which has a length of B sin . If P is a whole number of wavelengths then the radio waves detected at the two telescopes are in phase with each other and the combined signal has a maximum intensity. This is known as constructive interference. If P is a whole number of half wavelengths, then the radio waves are out of phase and cancel each other. The combined signal has a minimum intensity. This is destructive interference. Combining the signals
For a path difference of P, there is a corresponding phase difference between the waves which arrive at the two telescopes. This can be written as = B cos 2 /. As the earth rotates the direction to the source ( ) changes and both P and change with time. For a point source, the intensity of the correlated signal varies sinusoidally between maximum and minimum values. The variations in intensity are known as interference fringes. The separation of the fringes is a measure of the angular resolution of the interferometer. Measuring fringes
For a baseline of length B, the angular resolution is given by: Resolution (R) (arcsec) = 2 x 10 5 x wavelength observed = Projected baseline length Bsin Because B can be made very large, R can be made very small. Most radio arrays have angular resolutions between 0.1 and 10 arcseconds. In Very Long Baseline Interferometry (VLBI), telescopes located in different parts of the world are used to give baselines of 1000s of kilometres and angular resolutions of milli-arcseconds - vastly smaller than for optical telescopes! Angular Resolution of an Interferometer
In the correlator the signals are multiplied together and are averaged over a sampling time of typically 20 to 30 seconds. The correlator is a powerful piece of electronics and software which is at the heart of any radio interferometer or radio array. The correlated signal is called the source visibility - this has two parts: The visibility amplitude is a measure of the detected flux density from the source. The visibility phase provides information on the source position. The visibility amplitudes and phases are written as data onto computer disks where they are stored for later analysis. The source visibility
Single-baseline interferometers can be used to measure the positions of unresolved sources, to an accuracy comparable to the angular resolution. To make an image of a more complex radio source, it is necessary to use an array of radio telescopes which has a number of baselines of different lengths. The longer baselines resolve the small-scale structure in the source. The shorter baselines provide information on the larger scale structures. The technique of using arrays of radio telescopes is called aperture synthesis interferometry. Why use arrays?
To illustrate how an array of radio telescopes works, consider some of the properties of the Australia Telescope Compact Array (ATCA). The ATCA has six telescopes and 15 different baselines. In general, an array of n telescopes has n(n-1)/2 baselines. Each of the telescopes has a diameter of 22 m. The Australia Telescope Compact Array
This photograph shows an aerial view of the site of the ATCA which is located at Narrabri in northern New South Wales. Five radio telescopes can be seen on the three-kilometre arm of the array. These telescopes can be moved by driving them to different stations along a railway track. The track is aligned in an east-west direction. The Compact Array also has an additional 22-m antenna which is not seen here but which provides baselines up to 6 km. 3-km Railway Track
By driving the telescopes to different stations on the railway track the ATCA can be used in a number of different configurations. Each configuration corresponds to one set of baseline lengths. The full range of possible baselines covers distances between 30 m and 6 km. At present the ATCA is used to take observations at wavelengths of = 3, 6, 13 and 20 cm. It is currently being upgraded to work at millimetre wavelengths. Properties of the ATCA
Observations taken with the ATCA are used to make images of the radio emission from astronomical sources such as stars, supernovae remnants or distant quasars. For a short observation the ATCA gives a good angular resolution in one direction but very poor angular resolution in other directions. In effect the source is resolved in one dimension only. The problem of resolving a source in two-dimensions can be solved by using the rotation of the earth to observe the source from different directions. Resolving a source in two dimensions
As the earth rotates the direction of the baselines as seen from the source changes. Over an interval of twelve hours, each baseline will have all possible orientations relative to the source. Note that it is the projected baseline that changes. The actual baseline (B) remains constant. Using the earth’s rotation Source T1 T2 Earth
As seen from the source, each baseline traces out an ellipse with one telescope at the centre of the ellipse: The u-v plane The projected baseline can be specified using u-v coordinates. u gives the east-west component of the baseline. v gives the north- south component of the baseline. The projected baseline is given by Bsin = (u 2 + v 2 ) 1/2 v u T1 T2
For an east-west array of telescopes like the ATCA, the baselines trace out a set of concentric ellipses in the u-v plane. Lets look at some examples for sources at different declinations in the sky: The next three slides show the u-v ellipses that would be obtained from observations taken with the ATCA at = 6 cm, for a source at a declination of -85, -40 and -10 degrees respectively. Examples of u-v diagrams
u-v example 1: declination = -85 degrees For sources at very southern declinations, the u-v ellipses are almost circular. This means that the angular resolution is the same in every direction. In these plots the u and v distances are given in units of kilo-wavelengths. At 6 cm, 100 k is equal to 6 km. Complete ellipses like these are obtained from a 12-hour observation. The diagram shows 15 different ellipses, with one ellipse for each of the baselines of the Compact Array. The largest and smallest ellipses correspond to the longest and shortest baselines respectively.
u-v example 2: declination = -40 degrees At lower declinations, the u-v ellipses are flattened in the north-south (v) direction. The angular resolution is largest in the north-south direction.
u-v example 3: declination = -10 degrees For sources at low declinations, the u-v ellipses are highly flattened. The angular resolution is very poor in the north-south direction. For low declinations a source cannot be observed for a full 12 hours, so there is a gap in the u-v coverage. Gap
The basic principle of radio interferometry is that the measured interference patterns can be used to recover information on the source structure and size. The source visibilities for each baseline are typically sampled every 30 seconds throughout the observations of a radio source. u-v diagrams, such as those shown earlier, show how well the u-v plane has been sampled. Sampling the u-v plane
In principle the best possible image would be obtained by sampling the source visibilities at every point in the u-v plane. In practise this is not possible and sophisticated analysis techniques are used to ‘fill in the gaps’. The u-v coverage, shown by the ellipses, is related to the image quality that can be achieved. An array of radio telescopes does not directly obtain an image of a radio source. The image can however be ‘reconstructed’ by analysing the interference patterns detected on the different baselines. Making an image
The details of how a radio image can be obtained from the source visibilities is discussed in Module 13, activity 2. To illustrate the relationship between the image plane and the visibility plane, lets consider the visibility amplitudes for sources with simple spatial structures. Each of the visibility plots shown on the next few slides were obtained using a model source at a declination of -80 degrees to simulate the visibility amplitudes obtained in 12 hours with the ATCA at a wavelength of 6 cm. Some visibility examples
First consider a single point source. Case 1 - A point source An image of a point source. For this model the source has a flux density of 1 Jy. North Visibility Amplitude (Jy) Projected baseline length =(u 2 + v 2 ) 0.5 (k ) 1.0
The visibility amplitudes for a point source are constant. This is because the source size is very small compared to the angular resolution on each of the baselines. The visibility amplitude is the same as the total flux density of the source. Case 1- a point source cont. Angular resolution A very small source
Case 2 - a small source In this model the source has a total flux density of 1 Jy but is slightly extended with a size of one arcsecond (this model uses a Gaussian brightness distribution). An image of a slightly extended source. For this model the source has a total flux density of 1 Jy. One arcsecond radio source
Case 2 - a small source cont. Visibility Amplitude (Jy) (u 2 + v 2 ) 0.5 (k )
For a slightly extended source, the visibility amplitudes decrease with increasing baseline length. The largest amplitudes are measured for the shortest baselines. On the longest baseline at (100 k ), the visibility amplitude drops to about half of the peak value. This source is unresolved on the shorter baselines but is partially resolved on the longer baselines. Case 2 - a small source cont. long baselines short baselines Source (size = 1 arsecond)
Case 3 - a larger source An image of a larger extended source. The source has a total flux density of 1 Jy. 3 arcseconds In this model the source again has a total flux density of 1 Jy but has a larger size of three arcseconds.
Case 3 - a larger source cont. 1.0 (u 2 + v 2 ) 0.5 (k ) Visibility Amplitude (Jy)
Compare the visibility plots for case 2 and case 3. For the larger source, the visibility amplitudes decrease more steeply as the baselines increase in length. This source is well resolved. Note that almost no emission is detected on the longest baselines. Case 3 - a larger source cont. long baselines shortest baseline Source (size = 3 arseconds)
To end this discussion consider two point sources which are separated from each other by one arcsecond in an east-west direction. Each of the sources has a flux density of 1 Jy. Case 4 - two point sources For this model the diagram on the next slide shows how the visibility amplitudes vary with time for the five longest baselines of the ATCA. 1 arcsec
Case 4 - two point sources cont. Visibility Amplitude (Jy) Time from start of observation (hours) Amplitude variations for a 6-km baseline. Amplitude variations for a 3-km baseline.
For this model, the visibility amplitudes decrease during the first six hours of observing but then increase again. The maximum detected emission of 2 Jy corresponds to the total flux density of the two sources. For some baseline directions the wavefronts from the two sources combine in phase and the visibility amplitude from the correlated signal has a maximum value. For other directions the wavefronts from the two sources partly cancel each other giving smaller visibility amplitudes. Notice that the strongest variations occur for the longest baselines where the source is most resolved. Case 4 - two point sources cont.
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Image Credits The Australia Telescope Compact Array 13-cm radio emission from Jupiter Image credit: G. Dulk, Y. Leblanc, R. Sault, R. Hunstead Effelsberg 100-m radio telescope Aerial view of the Compact Array Photo credit: Stewart Duff, CSIRO