signal is fed both to a detector operating synchronously with the beam switching and to an acousto-optical spectrometer (AOS) for spectrum analysis.

12.8.2 Antenna Temperature of Radio Sources

The flux S of a radio source is calculated by integrating the brightness BS over the solid angle VS covered by the source:

VS

The unit of flux is jansky (Jy); one jansky is 10−26 Wm−2 Hz−1.

Some radio sources are like points in the sky, and some sources are extended. If the radio source is a point source and in the middle of the

For an extended source, the flux S has to be replaced with the flux So observed by the antenna. So is obtained by weighing the right side of (12.22) with the normalized directional pattern Pn (u, f). If the brightness of the radio source is constant over the whole antenna beam, the received power is

where VA = ee4p Pn (u, f) d V is the solid angle of the beam. Now the observed flux is So = BS VA .

The received power may be written using the antenna noise temperature

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If the brightness temperature of the source, TB , is constant over the whole beam, then TA = TB . For a small source (Pn ≈ 1 over the whole source), the antenna noise temperature is

Above, the influence of the atmospheric loss was not taken into account. Because the fluxes of radio sources are values defined outside the atmosphere, the measured results have to be corrected with the attenuation of the atmosphere.

Example 12.6

A point source having a flux of 2 Jy is measured with a 13.7-m radio telescope. Find the antenna noise temperature produced by the source and the required integration time t . The attenuation of the atmosphere is L = 0.8 dB, the aperture efficiency is hap = 0.6, the noise temperature of the Dicke receiver is TR = 100K, and the bandwidth is D f = 300 MHz.

Solution

The physical area of the aperture is A = p D 2/4 = 147.4 m2. The effective area A ef = hap A = 0.6 × 147.4 m2 = 88.4 m2. The flux at the antenna is S = 2 × 10−0.08 Jy = 1.66 Jy. From (12.26), the antenna noise temperature

produced by the source is TA , source = 88.4 × 1.66 × 10−26/(2 × 1.38 × 10−23 )K = 53 mK. The sensitivity of a Dicke radiometer is DT =

2Ts /√tDf . The antenna noise temperature produced by the atmosphere is TA , atm = (1 − 1/L ) Tphys = (1 − 10−0.08 ) × 290K = 49K, assuming that the physical temperature of the atmosphere, Tphys , is 290K. Thus, the system

noise temperature is TS = TA , atm + TR = 49K + 100K = 149K. The integration time depends on the required S /N (note that now signal is also noise). S /N = 1 or TA = DT is achieved if t = (2TS /TA )2/Df = 0.11 second. The integration time needed for S /N = 10 is 100 times longer, nearly 11 seconds.

12.8.3 Radio Sources in the Sky

The radio sky is very different from the sky we see at optical wavelengths. Point sources, radio ‘‘stars,’’ are not ordinary stars, which are relatively weak emitters of radio waves. The most significant similarities are the plane and the center of the Milky Way, which can be seen clearly in both optical and radio pictures.

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Microwave Anisotropy Probe (MAP), launched in 2001, and Planck Surveyor, scheduled for launch in 2007, is to measure these fluctuations with a much better angle resolution and with a better receiver sensitivity.

Although stars are weak radio sources, the Sun is an exception because of its vicinity. The radiation from the Sun at frequencies higher than 30 GHz resembles the radiation of a blackbody at a temperature of about 6,000K. At lower frequencies the brightness temperature may be as high as 1010 K and depends on the activity of the Sun. When the Sun is active and there are plenty of sunspots, there are variations in the intensity of radiation. The sunspots are a source of slow variations and the flares are a source of rapid variations.

The planets and the Moon radiate almost as a blackbody. Jupiter is an exception: Below microwave frequencies it radiates more than a blackbody at the same temperature. The intensity of Jupiter’s radiation varies in a complicated manner and is related to the position of its moon Io. Before the time of spacecraft, planets were studied using radar techniques. For example, the rotation times of Mercury and cloud-covered Venus were determined with radar in the 1960s. The surface of Venus was mapped more accurately in the beginning of the 1990s with SAR on the Magellan spacecraft. The rings of Saturn, its moon Titan, and asteroids have also been studied with radar.

Gas and molecular clouds, remnants of supernovas, and pulsars are radio sources in our galaxy. The continuum radiation of the Milky Way consists of synchrotron radiation and thermal radiation from ionized hydrogen. The synchrotron radiation dominates at frequencies lower than about 1 GHz and the thermal radiation at higher frequencies.

At 1,420 MHz (l = 21 cm) interstellar neutral hydrogen emits a spectral line, which has been used to map the structure of the Milky Way. By measuring radial velocities of hydrogen clouds in different directions using the Doppler shift, it has been concluded that we live in a spiral galaxy. Even the center of the Milky Way can be studied using radio waves, which penetrate through dust clouds.

In addition to hydrogen, many different molecules, both inorganic and organic, have been observed in interstellar clouds, in which new stars are born. More than 80 different molecules have been found, the most complicated of which has 13 atoms [14]. The line spectra of molecules are produced by changes in the rotational energy states and occur at millimeter and submillimeter wavelengths. Lines may be either emission or absorption lines. An absorption line is produced when a cloud absorbs a narrow band of frequencies from continuum radiation coming from background. The measurement of