In Chapter 2, I recount a brief history of the discovery of the major maser species. This chapter is designed to be understood by a reader with little mathematical knowledge. For those more interested in the technical details relating to radio telescopes, I refer the reader forward to Chapter 4, and particularly to Section 4.1.

During the late 1950s, technological developments allowed radio telescopes to observe at frequencies above 1 GHz (the L-band in radar terminology). A key L-band transition is the ‘spin-flip’ line of atomic hydrogen at 1421 MHz, which allowed astronomers to map the neutral hydrogen content of the Galaxy. Clouds excited by the formation of massive stars are photoionized, rather than neutral, and ionized hydrogen emits a continuous spectrum of radiation through the thermal bremsstrahlung process (see Section 2.9.1). As this process is thermal, it has a spectrum which rises with frequency at radio wavelengths if optically thick (see Eq. (4.7)), making it stronger at L-band relative to non-thermal emission, when compared with earlier observations at lower frequencies. Non-thermal radiation processes typically have a spectrum which decays as a power-law with frequency in the radio region. A catalogue of sources containing ionized hydrogen, comprising mostly massive, star-forming, Galactic gas clouds, was constructed by Westerhout (1958) from continuum observations at 1390 MHz, and its sources were classified by a W-number (for example W49), a nomenclature which has continued to be used up to the present day, and in particular for the case study of W3(OH) in Section 2.9.

The theory of astrophysical masers can be neatly divided into two problems. One is the transfer of radiation through the medium containing the active (maser generating) molecules, and the other is the molecular physics required to calculate the inversion. Most of the complexity of maser theory arises because these problems are coupled. The molecular physics problem appears to be local: we calculate a population inversion at a position in space, which depends on the physical conditions at that point. Unfortunately, these conditions include the radiation field, which requires a solution to the obviously non-local problem of radiation transfer. In turn, radiation transfer requires a knowledge of the populations of the molecular energy levels at all points along a ray and, therefore, of a solution of the molecular physics problem along the path of the same ray.

Non-LTE physics

For gases which are not in local thermal equilibrium (LTE), we must calculate the populations of energy levels by means other than Boltzmann's formula. We do, however, assume that there are sufficient collisions to maintain a Maxwell–Boltzmann distrubution of molecular speeds. For the moment, we also assume that the molecular populations can be accurately calculated from a set of kinetic master equations – often called ‘rate equations’. These equations simply state that, in a steady state, the net population flow into any energy level from all the others is zero.

At present, there are a number of radio astronomy projects in progress which promise to revolutionize our understanding of astrophysical masers and their environments. Masers form only a small part of the impressive science programmes for these new telescopes, so this chapter contains a considerable amount of general material about the instruments and their capabilities.

EVLA

Introduction to the EVLA

The Expanded Very Large Array (EVLA) is a two-phase development of the existing VLA, situated in New Mexico, USA, and operated by the National Radio Astronomy Observatory. The general capabilities of the EVLA can be found at the website http://www.aoc.nrao.edu/evla/. Phase 1 developments are technological, upgrading the existing array to a wide-band system, whilst Phase 2 involves the construction of new antennas, to provide significantly improved spatial resolution, and improved linkage to the VLBA. The technological developments are similar to those of e-MERLIN (see Section 10.2).

Continuum sensitivity improvements range from a factor of 5 at low frequencies to 20 or more above 10 GHz. This is important for maser, and all spectral line, observations, because the spectral line observations rely on continuum sources for calibration. Spectral line sensitivity increases in Phase 1 are modest below 10 GHz, but up to a factor of 3 at higher frequencies. The EVLA will also move to a wide-band receiver system with fibreoptic cabling and digital electronics, allowing complete frequency coverage from 1 to 50 GHz, with a bandwidth of up to 8 GHz per polarization.

Except in very simple cases, it is not possible to solve the coupled molecular physics and radiation transfer problems for masers, or their pumping radiation, analytically. For more realistic problems, we need to resort to numerical solutions. There are many general-purpose radiative transfer codes available. However, a substantial fraction of these require modification to work in situations that may produce masers: inverted populations yield negative absorption coefficients, optical depths and source functions: situations that will cause many codes to fail.

Large velocity gradient approximation

The large velocity gradient (LVG) or Sobolev approximation (Sobolev, 1957) is a means of casting the radiative transfer problem into an entirely local form. In LVG, the integrations that appear in the formal solution of the radiative transfer equation can be carried out, so the line mean intensity can be expressed explicitly as a function of the energy-level populations from the same transition. Elimination of the mean intensities in favour of the population expressions leads to a set of master equations which are non-linear algebraic equations in the populations. The LVG approximation is therefore not really a numerical method, but a clever approximation that allows much simpler numerical methods to be used than suggested by the original problem.

Theory

We begin by selecting the radiation transfer equation for transport along a ray element ds, Eq. (3.78). We do not, at present, assign any particular geometry to the problem, and one of the greatest advantages of the LVG approximation is that it is almost geometry free.

Masers have been detected in a wide variety of astrophysical environments. Perhaps the most astounding feature is the range of scales: the smallest maser environments are objects familiar to us from our own Solar System – comets and planetary atmospheres – whilst the largest masers form in molecular tori around the nuclei of certain galaxies, and may be up to 1 kpc (∼3 × 1019 m) in size. Some of these environments are so violent that, in a naive view, its is difficult to see how the necessary molecules can survive. However, it is the extreme nature of the environments that aids the pumping of masers. Often, we can deduce that gas molecules have motions characteristic of one temperature (a local kinetic temperature) whilst the radiation which is present is characteristic of a different, and usually higher, temperature. Maser molecules cannot attain a distribution of population amongst their energy levels which represents an equilibrium at either temperature, and these nonlocal-thermodynamic-equilibrium (NLTE) conditions allow population inversions to form.

Galactic star-forming regions

The formation of stars from the gravitational collapse of clouds of interstellar gas remains, in its details, one of the great unsolved problems of astrophysics. Our Galaxy, the Milky Way, is a spiral type, which is still forming stars at a significant rate at the current epoch; not all galaxies do. Elliptical and lenticular galaxies have very little interstellar gas compared with spirals, and are forming very few new stars. Within the spiral category, ‘early’ types (Sa, SBa), with large nuclei and tightly wound arms, are comparatively gas-poor compared with ‘late’ types (Sc, SBc), with relatively smaller nuclei and more open spiral arms.