Chris Salter NAIC/Arecibo Observatory Technical Fundamentals of Radio Astronomy

The Atmospheric Windows τ (Transparency = e –τ )‏ 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!

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!”

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

Telescope Beam Pattern The response of the telescope to signal power arriving from a direction (θ, Φ) is known as the BEAM PATTERN, or the POWER POLAR DIAGRAM, P(θ, φ). We normalize the response such that, P(0,0) = 1.0 The pattern has a MAIN BEAM and SIDELOBES. The sidelobes in the rear 2π 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 × λ/D radians, where λ is the wavelength. NOTE: D/λ = Number of wavelengths across the telescope.

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 MHz 0.5 arcmin Wavelength Frequency HPBW HPBW of the Arecibo 305-m Telescope

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 dΩ Area = dA Considering the energy in a frequency band of width, dυ, about a central value, υ, arriving per sec from the direction (x,y) in solid angle, dΩ. Then the Intensity, I(x, y) is given by; I(x,y,υ,t) = lt dE(x,y,υ,t) dA,dΩ,dυ,dt → 0 cosθ dA dΩ dυ dt (x, y )‏ NOTE: dE/dt is the power received from dΩ on area dA in bandwidth dυ. 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 dΩ 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 υ 2 = 2 k T B (where c = speed of light c 2 λ 2 and k = Boltzmann's Constant)‏

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 υ, we use the power received from the whole source on unit area, per Hz of bandwidth. This we call the FLUX DENSITY, S(υ, t). Integrating over solid angle; S(υ, t) = ∫ I(x, y, υ, t) dΩ source Note that for our tiny piece of sky, dΩ, S = I dΩ = dE, so the units are W m -2 Hz -1 dA dυ 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) = 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!

Distance Dependencies Suppose we observe a galaxy of radius, r, at distance, D, Then we see the galaxy as subtending a solid angle of πr 2 / D 2. So, dΩ α D -2 Now, the energy, dE received from the galaxy α D -2 (inverse square law)‏ And as I = dE / (dA dΩ dυ 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 dυ dt) so, S falls as the inverse-square of the distance. 2 × r D

Effective Area of a Telescope A Point Source is one that has an angular size, θs << HPBW of the antenna. Its flux density is S(υ) = dE/(dA dυ dt), so the power collected by our telescope can be written as S(υ) A eff (υ) Δυ, where Δυ is the receiver bandwidth, and A eff (υ) is called the Effective Area of the telescope. Note that a single radio receiver can only collect the power from one of the two polarizations of the incoming signal. Hence it can only collect ½ S(υ) A eff (υ) Δυ. Suppose that after observing a point source, we replace the receiving dipole by a resistor whose temperature is adjusted to a value T A, where the noise power from the resistor equals the power previously received from the point source. Now the power received from a resistor at a temperature T = k T Δυ. Hence; k T A Δυ = ½ S(υ) A eff (υ) Δυ and, A eff (υ) = 2 k T A,where T A is called the Antenna Temperature. S(υ)‏ Hence, if we measure a source of known flux density, we can calculate A eff. If A P is the physical area of the antenna, we define its Aperture Efficiency to be; η A = A eff /A P < 1.0

A Simple Radio Receiver Front-end IF Stage Back-end The preamplifier is very important as it provides most of the noise against which we are trying to detect a radio source! The mixer changes the frequency of the received signal to a (usually) lower frequency. Most amplification occurs at the IF Stage, and a “Standard IF” can be used for received signals of all frequencies. A Square-Law Detector is used so: Output voltage α(Input Voltage) 2 α Input Power The integrator sums up the detector output, “beating down” the noise level in the process. The data are recorded for subsequent analysis. The celestial source provides a “noise-power” giving Antenna Temperature = T A.

Receiver Noise RECEIVER NOISE TEMPERATURE, T R, is given by P R = k T R Δ υ 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, (Δυ τ) 0.5 where Δυ is the receiver bandwidth (Hz), and τ 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

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; φ = (2π b cos θ) / λ, where λ is the wavelength. This produces a fringe pattern, with maxima at cos θ = n λ / b If b = 30 km and λ = 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.

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 (ΝΜ, USA)‏ Radio Interferometers

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)‏