IOP PUBLISHING REPORTS ON PROGRESS IN PHYSICS Rep. Prog. Phys. 71 (2008) 066901 (32pp) doi:10.1088/0034-4885/71/6/066901 High resolution radio astronomy using very long baseline interferometry Enno Middelberg1 and Uwe Bach2 1 Astronomisches Institut, Universitat¨ Bochum, 44801 Bochum, Germany 2 Max-Planck-Institut fur¨ Radioastronomie, Auf dem Hugel¨ 69, 53121 Bonn, Germany E-mail: [email protected] and [email protected] Received 3 December 2007, in final form 11 March 2008 Published 2 May 2008 Online at stacks.iop.org/RoPP/71/066901 Abstract Very long baseline interferometry, or VLBI, is the observing technique yielding the highest-resolution images today. Whilst a traditionally large fraction of VLBI observations is concentrating on active galactic nuclei, the number of observations concerned with other astronomical objects such as stars and masers, and with astrometric applications, is significant. In the last decade, much progress has been made in all of these fields. We give a brief introduction to the technique of radio interferometry, focusing on the particularities of VLBI observations, and review recent results which would not have been possible without VLBI observations. This article was invited by Professor J Silk. Contents 1. Introduction 1 2.9. The future of VLBI: eVLBI, VLBI in space and 2. The theory of interferometry and aperture the SKA 10 synthesis 2 2.10. VLBI arrays around the world and their 2.1. Fundamentals 2 capabilities 10 2.2. Sources of error in VLBI observations 7 3. Astrophysical applications 11 2.3. The problem of phase calibration: 3.1. Active galactic nuclei and their jets 12 self-calibration 7 2.4. Polarization 8 3.2. Stars 21 2.5. Spectral line VLBI 9 3.3. Results from astrometric observations 23 2.6. Pulsar gating 9 4. Conclusions 26 2.7. Wide-field limitations 9 Acknowledgments 26 2.8. VLBI at millimetre wavelengths 9 References 27 1. Introduction of the sky at radio frequencies. The angular resolution and positional accuracies achieved in these observations are as high Very long baseline interferometry, or VLBI, is the technique as a fraction of a milli-arcsecond. by which radio telescopes separated by up to thousands of The radio regime was the first waveband accessible to kilometres are used at the same time for astronomical or astronomers after they had studied the skies only at optical geodetic observations. The signals are received and amplified wavelengths for hundreds of years. In the first half of the at the participating antennas, and are digitized and sent to a 20th century, rapid progress in high-frequency technology correlator, either by storing them on tape or disk for later facilitated access to radio wavelengths. Owing to the (then) shipment, or, more recently, by sending them over network relatively long wavelengths, radio observations even with large links. The correlator cross-correlates and Fourier transforms single telescopes had poor angular resolution of no better than the signals from each pair of antennas, and the result of this 10 arcmin, but after World War II the first interferometers process can be used to determine the brightness distribution emerged and increased the resolution to less than 1 arcmin. 0034-4885/08/066901+32$90.00 1 © 2008 IOP Publishing Ltd Printed in the UK Rep. Prog. Phys. 71 (2008) 066901 E Middelberg and U Bach Astronomers were puzzled that even at the highest resolution the corks are very close together, they will move up and down achieved with radio-linked interferometers (about 0.1 arcsec), almost synchronously; however, as their separation increases some radio sources appeared point-like. This fuelled the desire their motions will become less and less similar, until they move to use even longer baselines. completely independently when several metres apart. Going from directly linked interferometers to independent Radiation from the sky is largely spatially incoherent, elements required recording the data in some way and except over very small angles on the sky, and these assumptions processing them later, but once the technical hurdles were (with a few more) then lead to the spatial coherence function overcome, the angular resolution of these observations −2πiνs( r1−r2)/c increased dramatically: from 1967 to 1969, the longest Vν (r1, r2) ≈ Iν (s) e d. (1) baselines used in VLBI observations increased from 845 to 10 592 km, yielding an angular resolution of the order of Here s is the unit vector pointing towards the source 1 mas. Thirty years after the first systematic radio astronomical and d is the surface element of the celestial sphere. The observations had been carried out the resolution had increased interesting point of this equation is that it is a function of more than a million fold. For more detailed reviews on radio the separation and relative orientation of two locations. An interferometry and VLBI we refer the reader to chapter one in interferometer in Europe will measure the same thing as one Thompson et al (2001) and Kellermann and Moran (2001). in Australia, provided that the separation and orientation of the Though many important discoveries had been made early interferometer elements are the same. The relevant parameters on, VLBI observations remain indispensable in many fields here are the coordinates of the antennas when projected onto a of astrophysical research. They will benefit much from plane perpendicular to the line of sight (figure 1). This plane improvements in computer technology, in particular from has the axes u and v, hence it is called the (u, v) plane. Now, let faster (and cheaper) network links. us further introduce units of wavelengths to measure positions This paper gives a brief overview of how radio in the (u, v) plane. One then gets interferometry works, of the calibration and data processing −2πi(ul+vm) steps required to make an image and the various flavours and Vν (u, v) = Iν (l, m)e dl dm. (2) niches which can be explored. It then reviews recent progress in the research of various astrophysical phenomena which has This equation is a Fourier transform between the spatial been made possible with VLBI observations. coherence function and the (modified) intensity distribution in the sky, Iν , and can be inverted to obtain Iν . The coordinates u and v are the components of a vector pointing from the origin 2. The theory of interferometry and aperture of the (u, v) plane to a point in the plane, and describe the synthesis projected separation and orientation of the elements, measured in wavelengths. The coordinates l and m are direction cosines 2.1. Fundamentals towards the astronomical source (or a part thereof). In radio 2.1.1. The visibility function. ‘An interferometer is a device astronomy, Vν is called the visibility function, but a factor, for measuring the spatial coherence function’ (Clark 1999). Aν , is commonly included to describe the sensitivity of the This dry statement pretty much captures what interferometry interferometer elements as a function of angle on the sky (the is all about, and the rest of this section will try to explain what antenna response3). lies beneath it, how the measured spatial coherence function is −2πi(ul+vm) turned into images and how properties of the interferometer Vν (u, v) = Aν (l, m)Iν (l, m)e dl dm. (3) affect the images. We will mostly abstain from equations here and give a written description instead, however, some The visibility function is the quantity all interferometers equations are inevitable. The issues explained here have measure and which is the input to all further processing by the been covered in length in the literature, in particular in the observer. first two sections of Taylor et al (1999) and in great detail in Thompson et al (2001). 2.1.2. The (u, v) plane. We introduced a coordinate system The basic idea of an interferometer is that the spatial such that the line connecting the interferometer elements, the intensity distribution of electromagnetic radiation produced baseline, is perpendicular to the direction towards the source, by an astronomical object at a particular frequency, Iν , can be and this plane is called the (u, v) plane for obvious reasons. reconstructed from the spatial coherence function measured at However, the baseline in the (u, v) plane is only a projection two points with the interferometer elements, Vν (r1, r2). of the vector connecting the physical elements. In general, the Let the (monochromatic) electromagnetic field arriving visibility function will not be the same at different locations at the observer’s location r be denoted by Eν (r) . Itisthe in the (u, v) plane, an effect arising from structure in the sum of all waves emitted by celestial bodies at that particular astronomical source. It is therefore desirable to measure it at frequency. A property of this field is the correlation function at as many points in the (u, v) plane as possible. Fortunately, = ∗ two points, Vν (r1, r2) Eν (r1)Eν (r2) , where the superscript the rotation of the Earth continuously changes the relative ∗ denotes the complex conjugate. V (r , r ) describes how ν 1 2 3 The fields of view in VLBI observations are typically so small that the similar the electromagnetic field measured at two locations is. dependence of (l, m) can be safely ignored. Aν can then be set to unity and Think of two corks thrown into a lake in windy weather. If disappears. 2 Rep. Prog. Phys. 71 (2008) 066901 E Middelberg and U Bach m sky plane l Source v (u,v) plane u Geometric delay τ s Antenna 1 Antenna 2 From antenna 1 From antenna 2 b Playback Playback Amplifier Amplifier unit unit Delay Local Local Mixer Mixer compensation oscillator oscillator Correlator Sampler Sampler FFT Disk/Tape Disk/Tape Vν(u,v) Shipped to Shipped to correlator correlator Figure 1.