Radio astronomy is the study of radio radiation from celestial sources.  The radio range of frequencies $\nu$ or wavelengths $\lambda$ is loosely defined by three factors: atmospheric transparency, current technology, and fundamental limitations imposed by quantum noise.  Together they yield a boundary between radio and far-infared astronomy at frequency $\nu \sim 1$ THz  (1 THz $\equiv 10^{12}$ Hz) or wavelength $\lambda = c / \nu \sim 0.3$ mm, where $c \approx 3 \times 10^{10}$ cm s$^{-1}$ is the vacuum speed of light. The Earth's ionosphere prevents ground-based observations at frequencies below $\nu \sim 10$ MHz ($\lambda \sim 30$ m).

### Atmospheric Windows

The Earth's atmosphere absorbs electromagnetic radiation at most infrared, ultraviolet, X-ray, and gamma-ray wavelengths, so there are only two atmospheric windows, in the radio and visible wavebands, suitable for ground-based astronomy. The visible window is relatively narrow in terms of logarithmic frequency or wavelength; it spans the wavelengths of peak thermal emission from $T \sim 3000$ K to $T \sim 10000$ K blackbodies. Since we can see only visible light without the aid of instruments, early observational astronomy was limited to visible objects—primarily stars, clusters and galaxies of stars, hot gas ionized by stars (e.g., the Orion nebula in Orion's sword is visible as a fuzzy blob to the unaided eye on a dark night), and objects shining by reflected starlight (e.g., planets and moons). Knowing the spectrum of blackbody radiation, astronomers a century ago correctly deduced that stars having nearly blackbody spectra would be undetectably faint as radio sources, and incorrectly assumed that there would be no other astronomical radio sources. Consequently astronomers failed to pursue radio astronomy until cosmic radio emission was discovered accidentally in 1932 and followed up by radio engineers.

Ground-based astronomy is confined to the visible and radio atmospheric windows, frequency ranges of the electromagnetic spectrum in which most radiation can reach the ground.  The radio window is much wider than the visible window when plotted on logarithmic wavelength or frequency scales, so it includes a wide range of astronomical sources and emission mechanisms.  One Angstrom $\equiv 10^{-10}$ m $= 10^{-8}$ cm. Radio astronomers usually measure (and think in terms of) frequencies $\nu = c / \lambda$ instead of wavelengths $\lambda$.  Thus $\lambda = 1$ cm corresponds to $\nu = 30$ GHz.  Ionospheric reflection (not absorption) prevents photons with wavelengths $\lambda > 30 {\rm ~m} = 3 \times 10^{11}$ Angstroms from reaching the ground. Abscissa: Wavelength in Angstroms.  Ordinate: Altitude at which half of the incoming radiation is absorbed by the atmosphere.
Image credit

What physical processes limit the radio window? At the high-frequency end, vibrational transitions of atmospheric molecules such as CO2, O2, and H2O have energies $E = h \nu$  (where $h =$ Planck's constant $\approx 6.626 \times 10^{-27}$ erg s) comparable with those of mid-infrared photons, so vibrating molecules absorb most extraterrestrial mid-infrared radiation.  Lower-energy rotational transitions of atmospheric molecules define the fairly broad transition between the far-infrared band and short-wavelength limit of the radio window.  Ground-based radio astronomy is increasingly degraded at frequencies $\nu < 300$ MHz (wavelengths $\lambda > 1$ m) by variable ionospheric refraction, which is proportional to $\lambda^2$.  Cosmic radio waves having frequencies $\nu < 10$ MHz (wavelengths $\lambda > 30$ m) are usually reflected back into space by the Earth's ionosphere.  Total internal reflection in the ionosphere at longer wavelengths makes the Earth look like a silvery ball from space, like the glass face of an underwater wristwatch viewed obliquely.

Ultraviolet photons have energies close to the binding energies of the outer electrons in atoms, so electronic transitions in atoms account for the high ultraviolet opacity of the atmosphere. Higher-energy electronic and nuclear transitions produce X-ray and gamma-ray absorption.  In addition, Rayleigh scattering of sunlight by atmospheric dust at visible and ultraviolet wavelengths brightens the sky enough to prevent nearly all daytime optical observations.  Radio wavelengths are much longer than atmospheric dust grains and the Sun is not an overwhelmingly bright radio source, so the radio sky is always dark and most radio observations can be made day or night.

The atmosphere is not perfectly transparent at any radio frequency.  The figure below shows how the zenith (the direction directly overhead) opacity $\tau_{\rm z}$ varies with frequency during a typical summer night in Green Bank, WV, with a water-vapor column density of 1 cm, 55% cloud cover, and surface air temperature $T = 288{\rm ~K} = 15{\rm ~C}$.  The total zenith opacity (solid curve) is the sum of several component opacities (Leibe, H. J. 1985, Radio Science, 20, 1069):
(1) The broadband or continuum opacity of dry air (long dashes) results from viscous damping of the free rotations of nonpolar molecules.  It is relatively small ($\tau_{\rm z} \approx 0.01$) and nearly independent of frequency.
(2) Molecular oxygen (O$_2$) has no permanent electric dipole moment, but it does have rotational transitions that can absorb radio waves because it has a permanent magnetic dipole moment.  The atmospheric-pressure-broadened complex of oxygen spectral lines near 60 GHz (short dashes) is quite opaque ($\tau_{\rm z} \gg 1$) and prevents ground-based observations between about 52 GHz and 68 GHz.
(3) Hydrosols are liquid water droplets small enough (radius $\leq 0.1$ mm) to remain suspended in clouds.  Since they are much smaller than the wavelength even at 120 GHz ($\lambda \approx 2.5$ mm), their emission and absorption can be described by the Rayleigh approximation and their opacity (dot-dash curve) is proportional to $\lambda^{-2}$ or $\nu^2$.
(4) The strong water-vapor line at $\nu \approx 22.235$ GHz is pressure broadened to $\Delta \nu \approx 4$ GHz width.  The so-called "continuum" opacity of water vapor at radio wavelengths is actually the sum of line-wing opacities from much stronger water lines centered on infrared wavelengths.  In the plotted frequency range, this continuum opacity is also proportional to $\nu^2$.  Both the line and continuum zenith opacities (dotted curves) are directly proportional to the column density of precipitable water vapor (pwv) along the vertical line-of-sight through the atmosphere.  The pwv is conventionally expressed as a length (e.g., 1 cm) rather than a true column density (e.g., 1 gm cm$^{-2}$), but the two are numerically equivalent because the density of water is one in cgs units.

The zenith atmospheric opacity for a typical summer night at Green Bank. An opacity $\tau$ attenuates the power received from an astronomical source by the factor $\exp(-\tau)$.  The oxygen and dry-air opacities are nearly constant, while the water-vapor and hydrosol (water droplets in clouds) contributions vary significantly with weather.

The partially absorbing atmosphere doesn't just attenuate the incoming radio radiation; it also emits radio noise that can seriously degrade the sensitivity of ground-based radio observations.  If the total opacity is $\tau$, the atmospheric transparency is $\exp(-\tau)$ and emission from the atmosphere at kinetic temperature $T$ adds $\Delta T_{\rm s} = T (1 - \exp(-\tau))$ to the system noise temperature $T_{\rm s}$.  Radio astronomers use $T_{\rm s} \equiv P_\nu / k$, where $k =$ Boltzmann's constant $\approx 1.38 \times 10^{-16}$ erg K$^{-1}$, as a convenient measure of the noise power per unit bandwidth $P_\nu$.  The system noise temperature is normally much smaller than the atmospheric kinetic temperature $T \sim 300$ K, so the added noise from atmospheric emission degrades sensitivity more than pure absorption does. For example, emission by water vapor in the warm and humid atmosphere above Green Bank, WV precludes sensitive observations near the water-vapor line at $\nu \sim 22$ GHz (1 GHz $\equiv 10^9$ Hz) during the summer.  Green Bank can be quite cold and dry in the winter, allowing observations at frequencies approaching 115 GHz.

The Atacama Large Millimeter Array (ALMA) is being built on this extremely high (5000 m) and dry desert plain near Cerro Chajnator in Chile with low atmospheric opacity at frequencies up to about 1 THz. Image credit

The very best sites for observing at higher frequencies are exceptionally high and dry, with typical pwv < 0.1 cm.

The Atacama Large Millimeter Array (ALMA) will ultimately cover the ten frequency bands indicated by numbered horizontal bars.  The gaps between bands 8 and 9 and between bands 9 and 10 match frequency ranges with very low atmospheric transmission. Image credit

### Astronomy in the Radio Window

The radio window in exceptionally broad, spanning roughly five decades of frequency (10 MHz to 1 THz) and wavelength.  This breadth has both scientific and practical consequences:

• A wide variety of astronomical sources, thermal and nonthermal radiation mechanisms, and propagation phenomena can be studied at radio wavelengths.
• A wide variety of radio telescopes and observing techniques are needed to cover the radio spectrum effectively.

The radio window was used by astronomers before observations in other wavebands could be made with telescopes above the atmosphere, so early radio astronomy was a science of discovery and serendipity.  It revealed a "parallel universe" of unexpected sources never seen, or at least not recognized as being different from stars, by optical astronomers.   Major discoveries of radio astronomy include:

• Nonthermal radiation from our Galaxy and many other astronomical sources
• Cosmological evolution of radio galaxies and quasars
• Thermal spectal-line emission from cold interstellar gas atoms, ions, and molecules
• Coherent maser line emission from interstellar ions and molecules
• Coherent continuum emission from stars and pulsars
• Cosmic microwave background radiation from the hot big bang
• Neutron stars
• Indirect but convincing evidence for gravitational radiation
• Evidence for dark matter, deduced from the HI rotation curves of galaxies
• Extrasolar planets
• Gravitational lensing

Some features of this parallel universe are:

• It is often violent, emphasizing high-energy and explosive phenomena in radio galaxies, quasars, supernovae, pulsars, etc. in constrast to the steady light output of most visible stars.
• It is filled with sources ultimately powered by gravity instead of nuclear fusion, the principal energy source of visible stars.
• It is cosmologically distant.  Most continuum radio sources are extragalactic, and they have evolved so strongly over cosmic time that most are seen at lookback times comparable with the age of the universe.
• It can be very cold. The cosmic microwave background dominates the electromagnetic energy of the universe, but its 2.7 K blackbody spectrum is confined to radio and far-infrared wavelengths.  Cold interstellar gases emit spectral lines at radio wavelengths.
With the advent of astronomy from space, the entire electromagnetic spectrum has become accessible.  Many sources discovered by radio astronomers can be now studied in other wavebands, and new objects discovered in other wavebands (e.g., gamma-ray bursters) can be now be observed at radio wavelengths.  Radio astronomy is no longer a separate field; it is one facet of multiwavelength astronomy.  Even so, the radio band retains several unique astronomical and technical features.

The big picture: the electromagnetic spectrum of the universe (Dwek, E., & Barker, M. K. 2002, ApJ, 575, 7). The brightness $\nu I_\nu$ per logarithmic frequency (or wavelength) interval is shown as a function of the logarithm of the wavelength, so the highest peaks correspond to the most energetic spectral ranges.

Most of the electromagnetic energy of the universe is in the cosmic microwave background radiation left over from the hot big bang. It has a nearly perfect 2.73 K blackbody spectrum peaking at $\lambda \approx 1$ mm $= 10^3\,\mu$m.  The strong UV/optical peak at $\lambda \sim 1\,\mu$m is primarily thermal emission from stars plus a smaller contribution of thermal and nonthermal emission from the active galactic nuclei (AGN) in Seyfert galaxies and quasars.  Most of the comparably strong cosmic infrared background peaking at $\lambda \sim 100\,\mu$m is thermal re-emission from interstellar dust heated by absorbing about half of that UV/optical radiation.  The cosmic X-ray and gamma-ray backgrounds are mixtures of nonthermal emission (e.g., synchrotron radiation or inverse-Compton scattering) from high-energy particles accelerated by AGN and thermal emission from very hot gas (e.g., gas in clusters of galaxies).  By comparison, the cosmic radio-source background dominating at $\lambda > 10^6\,\mu$m is extremely weak.  Although they may be energetically insignificant, radio sources do trace most phenomena that are detectable in other portions of the electromagnetic spectrum, and modern radio telescopes are sensitive enough to detect extremely faint radio emission.

### What is Special About Long Wavelengths and Low Frequencies?

Many unique scientific and technical features of radio astronomy result from radio waves occupying the long-wavelength end of the electromagnetic spectrum. At macroscopic wavelengths ($\lambda \sim 0.3$ mm to $\sim 30$ m) large groups of charged particles moving together in volumes $< \lambda^3$ may produce strong coherent emission, accounting for the astounding radio brightnesses of pulsars.  Dust scattering is negligible because interstellar dust grains are much smaller than radio wavelengths, so the dusty interstellar medium (ISM) is nearly transparent. This allowed radio astronomers to see through the dusty disk of our Galaxy and discover the compact radio source Sgr A* powered by a supermassive black hole at the Galaxy center.

The
nucleus of the Milky Way Galaxy observed with the VLA at 1.3 cm and imaged with an angular resolution of 0.1 arcsec (Zhao, J.-H., & Goss, W. M. 1998, ApJ, 499, L163). Sgr A*, the bright unresolved radio source in the middle of this image, is powered by the supermassive ($3.7 \times 10^6$ solar masses) black hole in the Galactic center.

Low frequencies also imply low photon energies $E = h\nu$.  Thus radio spectral lines trace extremely low-energy transitions produced by atomic hyperfine splitting (e.g., the ubiquitous 21 cm line of neutral hydrogen at $\nu \approx 1.42$ GHz), the quantized rotation rates of polar molecules (e.g., carbon monoxide) in interstellar space, and high-level recombination lines from interstellar atoms.  The low values of the dimensionless quantity $h \nu / (k T) \ll 1$ at radio frequencies ensure that nearly everything is a thermal radio source at some low level.  Very cold astronomical sources may emit most strongly at radio wavelengths (e.g., the 2.73 K cosmic microwave background, interstellar gas at temperatures below 100 K).  In contrast, $h \nu / (k T) \gg 1$ for cold sources at optical frequencies, so the exponential high-frequency cutoff of the blackbody radiation spectrum ensures that essentially no optical photons are emitted and cold thermal sources are completely invisible.  For example, in the "spherical cow" approximation tradition in astronomy, a person is a 300 K blackbody with surface area of 1 m$^2$.  Such a person emits $\sim 10^{16}$ photons per second at radio frequencies below 10 GHz but only 0.01 photons per second at visible wavelengths $\lambda < 0.75 \,\mu$.
Stimulated emission is important when $h \nu / (k T) \ll 1$, and natural astrophysical masers ("maser" is an acronym for microwave amplification by stimulated emssion of radiation) are common.

Free electrons scatter electromagnetic radiation; this process is called Thomson scattering or Compton scattering. The Thomson scattering cross section per electron is $\sigma_{\rm T} \approx 6.65 \times 10^{-25}$ cm$^2$ at all frequencies, so sources with electron column densities $n_{\rm e} > \sigma_{\rm T}^{-1} \sim 10^{24}$ cm$^{-2}$ are called Compton thick'' and are hidden from view. Radio photons have energies much lower than the $\sim$ eV binding energies of electrons in atoms and molecules, so they can penetrate Compton thick sources. In contrast, such electrons do not appear bound to high-energy X-ray photons, so Compton thick sources (e.g., buried quasars'') are hidden from X-ray observations.

Radio synchrotron sources live long after their emitting electrons were accelerated to relativistic energies, so they provide long-lasting archaeological records of past energetic phenomena.  Plasma effects (scattering, dispersion, Faraday rotation, etc.) are strong enough to be useful tools for tracing interstellar electron densities and magnetic field strengths.   On the negative side, the fact that nearly everything emits radio radiation means radio astronomers must deal with large and fluctuating natural backgrounds of emission from the ground, from the atmosphere, and from their own equipment.

### Radio Telescopes and Aperture Synthesis Interferometers

Telescopes having very large diameters $D$ are required for good angular resolution $\theta \approx \lambda / D$ radians at long radio wavelengths. On the other hand, huge interferometers spanning $D \sim 10^4$ km are practical and large precision radio telescopes (e.g., telescopes with small rms surface errors $\sigma < \lambda/16$) can be built.  Paradoxically, the finest angular resolution for imaging faint and complex sources is obtainable at the long-wavelength (radio) end of the electromagnetic spectrum.  Interferometers also yield extremely accurate astrometry because interferometric positions depend on measuring time delays between telescopes rather than on the mechanical pointing errors of telescopes, and clocks are much more accurate than rulers.

The $D = 100$ m Green Bank Telescope (GBT) in West Virginia is the largest moving structure on land and weighs 16 million pounds ($\approx 7 \times 10^6$ kg), yet the rms deviation of its surface from a perfect paraboloid can be kept below $\sigma \approx 0.3$ mm, the thickness of three sheets of paper. The two semitrailers at the lower right are each 53 feet (16 m) long. The green grass and trees are not good signs for high-frequency observing; compare this with the ALMA and VLA site photos. Image credit

The 1 km configuration of the Very Large Array (VLA) of 27 25-m telescopes located on the semi-desert plains of San Augustin in New Mexico at an elevation of 7,000 feet (about 2100 m). The individual dishes can be moved to span $D =$ 1, 3.4, 11, or 36 km to synthesize apertures having those diameters and yield angular resolutions ranging from $\theta \approx 45$ arcsec at $\nu = 1.4$ GHz in the smallest configuration to $\theta \approx 0.04$ arcsec at $\nu = 43$ GHz in the largest.  Coherent (phase preserving) amplifiers allow the signals from each telescope to be combined with signals from the other 26 telescopes without loss of sensitivity, a requirement for making accurate images of faint extended sources. Image credit

The Very Long Baseline Array (VLBA) of 10 25-m telescopes extending 8000 km from St. Croix, VI to Mauna Kea, HI yields angular resolution as fine as $\theta = 0.00017$ arcsec, surpassing the resolution of the Hubble Space Telescope by two orders of magnitude. Image credit

Coherent (phase preserving) amplifiers are required for accurate interferometric imaging of faint extended sources because they allow the signal from each telescope in a multielement interferometer to be amplified before being split and combined with the signals from the other telescopes, rather than immediately being divided among the other telescopes.   The minimum possible noise temperature of a coherent receiver is $T \approx h\nu /k$ owing to quantum noise, which is proportional to frequency, so even the best possible coherent amplifiers at visible-light frequencies must have noise temperatures $T > 10^4$ K.  Aperture-synthesis interferometry at radio wavelengths provides unparalleled sensitivity, fidelity, resolution, and position accuracy.  This is a huge practical advantage of radio astronomy.

Multi-epoch VLBA position measurements of T Tau Sb, a companion of the well-known young stellar object T Tauri, allowed Loinard et al. (2007, ApJ, 671, 546) to determine its parallax distance with unprecedented accuracy: $d = 146.7 \pm 0.6$ pc, a significant improvement over the Hipparchos distance $d= 177^{+68}_{-39}$ pc, and even to detect accelerated proper motion.