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Chris Salter NAIC/Arecibo Observatory Technical Fundamentals of Radio Astronomy Slide 2 The Atmospheric Windows (Transparency = e ) Frequency (GHz) The Full Electromagnetic Spectrum Cm-wavelength Radio Spectrum Wavelength Ranges: Radio: 30 meter 1 millimeter = 3 10 4 :1 Optical: 0.3 0.75 = 2.5:1 If you can measure it with a ruler, then it's a RADIO WAVE! Slide 3 Observational Astronomy Q: In what way does Observational (Passive) Astronomy differ from Other Sciences? A: It is NOT experimental! E.g. Zoology: Rats in mazes: Planetary Radar: Particle Physics: The Larger Hadron Collider: BUT: In Observational Astronomy, What you see in what you get! Slide 4 Single-Dish Telescopes Telescopes GBT 100-m telescope (WV, USA) Effelsberg 100-m telescope (FRG) Arecibo 305-m telescope (Puerto Rico) IRAM 30-m mm-wave telescope (Spain) Ooty Radio Telescope 530 30 m (India) (1 arcmin = a Quarter at 100 yds) Single-Dish Radio Telescopes Slide 5 Telescope Beam Pattern The response of the telescope to signal power arriving from a direction (, ) is known as the BEAM PATTERN, or the POWER POLAR DIAGRAM, P(, ). We normalize the response such that, P(0,0) = 1.0 The pattern has a MAIN BEAM and SIDELOBES. The sidelobes in the rear 2 steradians are called the BACK LOBES. A design requirement is to minimize the sidelobes as they represent unwanted responses accepting power where you would like it rejected. The lower the sidelobes, the better the telescope can detect weak objects near a strong source, giving a higher DYNAMIC RANGE. Main-Beam Resolving Power: This is defined as the angular width of the main beam between directions where the response has fallen to one half of the maximum, called the HALF-POWER BEAMWIDTH (HPBW) or FULL-WIDTH HALF-MAXIMUM (FWHM). For a single-dish telescope of diameter, D; HPBW = 1.2 /D radians, where is the wavelength. NOTE: D/ = Number of wavelengths across the telescope. Slide 6 2.3 meter 130 MHz 37 arcmin 70 cm 430 MHz 11 arcmin 21 cm 1400 MHz 3.4 arcmin 13 cm 2300 MHz 2.0 arcmin 6 cm 5000 MHz 1.0 arcmin 3 cm 10000 MHz 0.5 arcmin Wavelength Frequency HPBW HPBW of the Arecibo 305-m Telescope Slide 7 Specific Intensity or Surface Brightness Intensity/Surface Brightness is the fundamental observable in radio astronomy representing the intensity of radio waves arriving at the Earth. Solid angle d Area = dA Considering the energy in a frequency band of width, d, about a central value, , arriving per sec from the direction (x,y) in solid angle, d. Then the Intensity, I(x, y) is given by; I(x,y,,t) = lt dE(x,y,,t) dA,d,d,dt 0 cos dA d d dt (x, y ) NOTE: dE/dt is the power received from d on area dA in bandwidth d. So, I is the power per unit area, per Hz from unit solid angle in the direction (x, y). The units of I are W m -2 Hz -1 ster -1. Brightness Temperature: Often Intensity is expressed as a brightness temperature T B, i.e. if the sky at d were replaced by a black body of temperature T B K, then at our observing frequency we would measure the same intensity. Luckily, most radio frequencies are sufficiently low, and T B sufficiently high that the Rayleigh-Jeans approximation holds, and; I = 2 k T B 2 = 2 k T B (where c = speed of light c 2 2 and k = Boltzmann's Constant) Slide 8 Flux Density We can scan our radio telescope over a radio source such as to measure its intensity distribution, and in the process produce a radio photograph (i.e. an image) of the source. To define a global parameter that characterizes the strength of the emission from our source at observing frequency , we use the power received from the whole source on unit area, per Hz of bandwidth. This we call the FLUX DENSITY, S(, t). Integrating over solid angle; S(, t) = I(x, y, , t) d source Note that for our tiny piece of sky, d, S = I d = dE, so the units are W m -2 Hz -1 dA d dt However, the flux densities of radio sources are so small that a more practical unit has been adopted. This is the Jansky, where; 1 Jansky (Jy) = 10 -26 W m -2 Hz -1 This looks pretty small, but in the 38 years since the Jansky was adopted things have moved along sufficiently that we can now detect sources whose flux densities are ~10 -5 Jy! Slide 9 Distance Dependencies Suppose we observe a galaxy of radius, r, at distance, D, Then we see the galaxy as subtending a solid angle of r 2 / D 2. So, d D -2 Now, the energy, dE received from the galaxy D -2 (inverse square law) And as I = dE / (dA d d dt), I is Distance Independent. (i.e. while a distant source looks smaller than a similar nearby one, it has the same intensity/surface brightness. In contrast, the flux density, S = dE / (dA d dt) so, S falls as the inverse-square of the distance. 2 r D Slide 10 Effective Area of a Telescope A Point Source is one that has an angular size, s Receiver Noise RECEIVER NOISE TEMPERATURE, T R, is given by P R = k T R PRPR SYSTEM NOISE TEMPERATURE, T S, is given by T S = T R +T A Q: How weak a source can we detect with our receiver? A: The answer is provided by the RADIOMETER EQUATION: Trms = Tsys, ( ) 0.5 where is the receiver bandwidth (Hz), and is the integration time (sec). A good rule-of-thumb is that a source will be detected if it provides T A > 5 T rms Slide 13 Interferometry If the biggest telescope in the World (Arecibo) has a resolution of ~1 arcmin, can we ever discover what the radio sky looks like at arsecond resolution, or finer? Yes Thanks to radio interferometery! Despite dealing with the longest wavelength electromagnetic waves, radio astronomy has provided our most detailed images of the Universe, achieving not only arcsec resolution, but even sub-milliarcsec resolution! Combining the voltages from 2 telescopes separated by a distance, b, there is a phase difference between them of; = (2 b cos ) / , where is the wavelength. This produces a fringe pattern, with maxima at cos = n / b If b = 30 km and = 3 cm, fringe maxima are separated by ~0.2 arcsec. If b = 6000 km, then the fringe separation is ~1 milliarcsec! While two antennas will give you a fringe pattern, combining the signals from many (N) telescopes separated by large distances, and allowing the Earth's rotation to move a radio source through their mutual N(N 1)/2 fringe patterns, allows us to make images of the sky with the angular resolution obtainable by a virtual single telescope whose diameter is that of the widest separation of any pair of telescopes present. Slide 14 Telescope Arrays Angular Resolution = ( / Separation) radians GMRT (India) VLBA (USA) VLA (NM, USA) (1 arcsec = a Quarter at 3.5 miles) (1 milliarcsec = a Quarter at 3500 miles) VLA (, USA) Radio Interferometers Slide 15 Very Long Baseline Interferometry When the telescopes in an interferometer array are separated by large distances, it was for many years impossible to directly combine their signals. The voltages from each telescope were recorded on magnetic tapes, and later disc packs, which are Fed-Exed to a central location where the signals from each antenna pair are cross- multiplied in a special Very Long Baseline Interferometry (VLBI) correlator. In recent years, real-time correlation has become possible by transmitting the signals directly to the correlation center via the internet eVLBI. A number of major VLBI arrays have come into being; Very Long Baseline Array (VLBA; USA) European VLBI Network (EVN; EEC) VLBI Space Observatory Project (VSOP; Japan)