Solution

The total power received is the power/area/Hz, multiplied by the frequency range (in Hz), and the surface area of the telescope:

This is 10 20 of the power of a 100 W light bulb. Note that the larger the dish, the larger the total power detected.

We have already seen that for making maps of extended sources, larger dishes are important because they provide us with better angular resolution. The weakness of radio sources gives us another reason for building large telescopes. A larger telescope intercepts more of the radiation, and allows us to detect weaker sources. A few large telescopes are shown in Fig. 4.27. The largest single dish is at the National Atmospheric and Ionospheric Center in Aricebo, Puerto Rico (Fig. 4.27a). The dish is made of a mesh surface that is set in a natural bowl. The holes in the surface are large enough that we can only use this dish for long wavelength observations. Also, the dish cannot be steered in any direction; it looks straight up. However, by moving the detectors around you can actually view a reasonable amount of sky. For many years, the largest fully steerable antenna was at the Max Planck Institut für Radioastromie in

Effelsberg, Germany (Fig. 4.27b). That telescope is 100 m in diameter. The inner 80 m has a surface made of solid panels so it can be used at wavelengths of a few centimeters. The outer 20 m is a mesh and is used to make the dish larger at longer wavelengths where diffraction is worse. The newest large telescope is the Byrd telescope, just being completed at the NRAO in Green Bank. It is a fully steerable 100 m telescope (Fig. 4.27c). It is designed so that more of the collecting area is used than in the German telescope. This is done in part by reducing the blockage by the support

Large radio telescopes. (a) The 300 m (1000 ft ) dish in Aricebo, Puerto Rico.The dish always points straight up, but moving the receiver to different off axis positions allows looking away from overhead. (b) The 100 m diameter telescope of the Max Planck Institüt für Radioastronomie, Effelsberg, Germany. It operates in azimuth and elevation. Azimuth is controlled by moving the whole structure on the circular track.As the telescope changes its elevation angle it deforms under gravity. However, it is designed to deform from one paraboloid into another, so only its focal length changes. (c), (d) The 100 m Byrd Telescope at the NRAO in Green Bank,WV. The offset arm to support receivers results in no blockage of the dish.This optimizes sensitivity and imaging quality.The telescope surface (c) and back-up structure (d) are shown. [(a) The Aricebo Observatory is part of the National Astronomy and Ionosphere Center operated by Cornell University under a cooperative agreement with the National Science Foundation; (b) MPIFR; (c),(d) NRAO/AUI/NSF]

structure. All of the surface is accurate enough for observations at wavelengths as short as 7 mm.

The detection of the radio waves takes place in a radio receiver. In general, the size of the receiver limits us to only one receiver operating on a telescope at a given time. This is equivalent to doing optical observations with only one detector in your CCD. At any given time, the telescope is receiving radiation from a piece of sky determined by the diffraction pattern of the antenna. If we want to build up a radio image of part of the sky, we must point the telescope at each position and take a separate observation. Recently, improvements in receiver technology have allowed limited multireceiver systems.

The receivers in radio astronomy are similar in concept to home radios. Like your home radio, the incoming signal is first mixed with a signal from a reference oscillator, and the resulting lower frequency beat note is then amplified. We change the frequency we are observing (like changing radio stations) by changing the frequency of the reference oscillator. However, the signals from astronomical sources are so weak by the time they reach us that receivers for radio astronomy must be much more sensitive than your home radio. Sometimes the receivers are cooled to a few degrees above absolute zero to minimize sources of background instrumental noise. Unlike bolometers, they do not simply detect all of the energy that hits them; they are also capable of preserving spectral information.

Just as with optical observations, in radio astronomy we can make continuum and spectral line observations. Continuum studies are like optical photometry. We tune our receivers to receive radiation over a wide range of frequencies, and we measure the total amount of power received. From this information, we obtain the general shape of the continuous spectrum (intensity vs. frequency).

In spectral line observations the radiation is detected in small frequency intervals, so the shapes of spectral lines can be determined. The spectrometers for radio observations have traditionally been large numbers of electronic filters, tuned to pass narrow frequency ranges. More recently, the ability of very fast computer chips has allowed for very flexible digital spectrometers. They measure the auto-correlation function of the incoming signal, which is the result comparing the signal with a slightly delayed version of the signal, and doing this for different delay times. We can think of this as the digital analog of the Michelson interferometer spectrometer discussed above. It therefore produces a Fourier transform of the spectrum. As with the Michelson interferometer, it is limited by its ability to measure this Fourier transform at only a finite range of time delays, with a step size limited by how fast we can run the computer. The computer speed determines the total bandwidth of the spectrometer, and the largest delay time determines the frequency resolution. By changing one or the other, we can adjust the bandwidth or the frequency resolution. That is why we say this is a very flexible system.

With either technology it is relatively easy to make high resolution spectral observations, with up to a few thousand frequency channels observed simultaneously. So, compared with optical observations, in radio observations we have to work harder to build up an image, but it is easier to make a spectrum at each position in our image.

One of the most important advances in radio astronomy in the last three decades of the 20th century has been the development of the millimeter (or shortest radio wave) part of the spectrum. As we will see throughout this book there are certain observations which are only possible at millimeter wavelengths. There also are some inherent benefits in working at millimeter wavelengths. If we can observe at 1 mm, for example, we can achieve the same angular resolution as at 10 cm, with a 100 times smaller dish! Of course, the dish must have a surface that is 100 times more accurate, meaning that it is hard to make a very large dish. This has restricted the size of millimeter telescopes to a few tens of meters in diameter, providing resolutions of ~10 to 20 arc sec at best.

At millimeter wavelengths the atmosphere blocks some of the incoming radiation (being somewhere between the totally clear radio and totally blocked infrared). This means that it is useful to put millimeter telescopes at high altitudes and dry sites (just as with optical or infrared telescopes). One of the first (and until its closure, in 2000, one of the most heavily used) millimeter telescopes was the 12 m telescope of the NRAO, located on Kitt Peak, Arizona, just below the site of the optical observatory (Fig. 4.28a). ESO

QqSIQIBqH Millimeter telescopes. (a) The NRAO 12 m telescope on Kitt Peak, Arizona. (b) The Swedish-ESO Submillimetre Telescope (SEST) on La Silla, Chile. (c) The 30 m telescope, Spain. (d) The Nobeyama 45 m telescope. [(a) Jeffrey Mangum, NRAO/AUI/NSF; (b) ESO; (c) IRAM;(d) Nobeyama Radio Observatory/National Astronomical Observatory of Japan]

QqSIQIBqH Millimeter telescopes. (a) The NRAO 12 m telescope on Kitt Peak, Arizona. (b) The Swedish-ESO Submillimetre Telescope (SEST) on La Silla, Chile. (c) The 30 m telescope, Spain. (d) The Nobeyama 45 m telescope. [(a) Jeffrey Mangum, NRAO/AUI/NSF; (b) ESO; (c) IRAM;(d) Nobeyama Radio Observatory/National Astronomical Observatory of Japan]

has operated the 15 m Swedish-ESO Submillimetre Telescope (SEST) at their optical site on La Silla, Chile (Fig. 4.28b). The largest millimeter telescopes are the 30 m telescope operated by French and German institutes, and located in Spain (Fig. 4.28c) and the Nobeyama 45 m telescope in Japan (Fig. 4.28d).

The problem of poor angular resolution for radio observations has been solved, in part, by using combinations of telescopes, called interferometers (Fig. 4.29). Interferometers utilize the information contained in the phase difference between the signals arriving at different telescopes from the same radio source. Any pair of telescopes provides information on an angular scale approximately equal (in radians) to the wavelength, divided by the separation between the two telescopes in a direction parallel to a line

Radio interferometer. Here only two telescopes are shown, but an interferometer with any number of telescopes can be treated as a number of pairs of telescopes. The separation between the telescopes produces a phase delay, which depends on the separation, d, and the position of the source.The phase difference can be detected, providing information about source structures whose angular size is approximately A/d (in radians). By using different telescope spacings and the Earth's rotation, information about structures on different angular sizes can be accumulated and eventually reconstructed into a map of the source.

Radio interferometer. Here only two telescopes are shown, but an interferometer with any number of telescopes can be treated as a number of pairs of telescopes. The separation between the telescopes produces a phase delay, which depends on the separation, d, and the position of the source.The phase difference can be detected, providing information about source structures whose angular size is approximately A/d (in radians). By using different telescope spacings and the Earth's rotation, information about structures on different angular sizes can be accumulated and eventually reconstructed into a map of the source.

connecting the two telescopes. To obtain information on different angular scales, it is necessary to have pairs of telescopes with different spacings. In addition, different orientations are needed. For this reason, interferometers generally have a number of telescopes. The Earth's rotation also helps change the orientation of any pair of telescopes, as viewed from the direction of the source. Unlike single dish observations, you don't have to point the telescope at different parts of the source to make a map.

To see some of the limitations of using interferometers to make images, we look a little more at how they work. We again look at any pair of telescopes, as indicated in Fig. 4.29. Before combining the signals from the two telescopes, we delay the signal from the nearer telescope by the extra time it takes the waves to reach the second telescope. That delay will change as we point the telescope pair at different angles above the horizon. This allows us to zero out the phase differ ence between signals from objects at the center of each field of view. But objects off the field center will have varying phase differences as we track the source across the sky. To extract a map of our field of view, we first multiply the two signals together (actually the delayed signal from the first telescope times the complex conjugate of the signal from the second telescope). This product is called the visibility. When you work out the details, the visibility turns out to be the Fourier transform of the two-dimensional intensity distribution on the sky, I(x, y). The visibility is a function of two variables (u, v), where u = (d/A)cos0o and v is defined for the corresponding angle in the perpendicular direction.

So, we measure the (2D) visibility at as many (u, v) points as possible, and then calculate I(x, y) by taking the 2D Fourier transform. Obviously, the more (u, v) points we can measure, the better we can estimate the visibility and the better we can estimate its Fourier transform. This is similar to the Michelson interferometer, discussed earlier in this chapter, where the more mirror positions at which we could measure the interference pattern, the more accurately we could compute the spectrum, which is the Fourier transform.

How do we measure many (u, v) points? For any pair of telescopes, we let the Earth's rotation change the elevation angle of the source, and also the orientation on the sky, changing how much of u and how much of v we are changing. So, if we do a series of observations, of say, 5 minutes each, and track a source for 8 hours, we can take many measurements. It also helps to have many telescopes. For N telescopes there are N(N—1)/2, independent pairs of telescopes, so, for large N, the number of pairs goes up roughly as N2. To make optimum use of these pairs, we don't simply have equally spaced telscopes, since every pair of spacing d will give redundant information. It is also useful to not have all the telescopes in a line,which would just give a lot of values of u or v, but not both. In general the shortest spacings give information on the large angular scales on the sky, and the longest spacing provide information on the smallest angular scales.

The most useful interferometer over the past several years has been the Very Large Array or VLA, near Socorro, New Mexico, operated by the NRAO

QQSlQIBQH Views of the Very Large Array (VLA), on the Plains of St Agustine (at an altitude of about 2.3 km) southwest of Socorro, New Mexico.There are 27 telescopes, each 25 m in diameter.At any instant there are 351 pairs of telescopes. Depending on the project, the spacings can be adjusted by moving the telescopes along railroad tracks. Moving all of the telescopes takes a few days and is done four times a year.The VLA is operated by the National Radio Astronomy Observatory. (a) The whole array. (b) The central section, showing a better view of the telescopes and the railroad tracks. (c) The transporter used to move telescopes on the tracks. [NRAO/AUI/NSF]

QQSlQIBQH Views of the Very Large Array (VLA), on the Plains of St Agustine (at an altitude of about 2.3 km) southwest of Socorro, New Mexico.There are 27 telescopes, each 25 m in diameter.At any instant there are 351 pairs of telescopes. Depending on the project, the spacings can be adjusted by moving the telescopes along railroad tracks. Moving all of the telescopes takes a few days and is done four times a year.The VLA is operated by the National Radio Astronomy Observatory. (a) The whole array. (b) The central section, showing a better view of the telescopes and the railroad tracks. (c) The transporter used to move telescopes on the tracks. [NRAO/AUI/NSF]

(Fig. 4.30). The VLA has 27 telescopes, 351 pairs (each 25 m in diameter), arranged in a 'Y configuration, to allow a wide range of both (u, v) values. Each arm of the Y is 21 km long. The telescopes are placed alongside railroad tracks, so that the telescope spacings can be changed, depending on the resolution needed for a particular project. These changes can take up to two weeks and are only done a few times a year. The shortest wavelength at which the VLA operates is 7 mm. It can be used for both continuum and spectral line observations. It has proved to be a powerful tool, providing images of radio sources, with many observing sessions ranging from a few minutes to a few hours. (The amount of data taken is so large that it takes the computers much longer to process the data than it does to observe.)

For observations requiring the best possible resolution, telescopes on opposite sides of the Earth are used. This is called very long baseline interferometry (VLBI). VLBI observations have provided angular resolutions of 10~4 arc seconds! In regular interferometry, the signals from the various telescopes are combined in real time, as the data comes in. In VLBI, signals at each telescope are recorded along with a time signal from a very accurate atomic clock. Later, the records are brought together, and the time signals are used

■ Arrangement of telescopes for the Very Long Baseline Array (VLBA), operated by the NRAO.There are ten telescopes, each 25 m in diameter. It operates down to a wavelength of 1 cm. [NRAO/AUI/NSF]

to coordinate the records from different telescopes, and the interferometry is then done by computer. To provide a dedicated group of telescopes for VLBI, the NRAO has recently built the Very Long Baseline Array (VLBA), which extends over much of North America (Fig. 4.31).

The success of interferometry and the importance of millimeter observations have led astronomers to begin working with millimeter interferometers. Millimeter waves provide many technical challenges for interferometry. For example, the effects of the Earth's atmosphere on the millimeter signals are important. Following the demonstration of successful millimeter interferometers operated by Caltech and Berkeley, the NRAO has started development of the Atacama Large Millimeter Array (ALMA), shown in Fig. 4.32. The final details are still being worked out, but the array, which is being built in collaboration with ESO and the Chilean government, will have approximately 75 telescopes, each approximately 12 m in diameter. They will work down to a wavelength of 0.8 mm. In order to get around atmospheric problems, a very high (5000 m) dry site in the Atacama Desert in Chile has been chosen. It is expected that operation will start in 2010.

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