Extremely sensitive radio telescopes can be made by hooking up arrays of individual antennas spread out over large areas – and the more antennas the better. However, sophisticated computer systems are needed to operate such arrays and computing costs grow rapidly with the number of antennas deployed. But now, two physicists in the US say that these costs can be reduced significantly if the antennas are arranged in hierarchical patterns. In particular, they say that some of the science goals of radio astronomers' next mega project, the Square Kilometre Array, could be met for a fraction of its current cost estimate.

Many scientific objectives in radio astronomy require the construction of more sensitive telescopes. These include the detection of the distinctive emission at 21 cm from neutral hydrogen, which pervades the universe. By recording the distribution of neutral hydrogen at increasing redshifts through measurements at longer and longer wavelengths, astronomers will be able to create a 3D map of most of our observable universe.

But greater sensitivity requires greater collecting areas, which increases costs. Making ever larger single-dish telescopes becomes prohibitively expensive beyond a certain size, so astronomers instead build arrays of smaller dishes that have their outputs combined through interferometry; an approach that also provides higher resolution. To make measurements at the longest radio wavelengths, researchers are also constructing arrays of huge numbers of simple dipole antennas (similar to those used for FM radios).

Out on the tiles

Unfortunately, as the number of antennas, N, in these arrays increases, the computing power needed to process their signals rises, roughly as N2. This is because interferometry requires correlating the output of every pair of antennas within an array. Computing accounts for around half of the hardware cost of the Murchison Widefield Array currently being built in the Australian outback, which consists of 512 "tiles" of 16 antennas. For the larger arrays needed to carry out precision measurements of neutral hydrogen computers will therefore come to dominate hardware costs.

Researchers have attempted to overcome this problem in two ways. One is to partition an array into tiles of multiple antennas (as with the Murchison Widefield Array), with the output from each tile rather than every single antenna being processed. This reduces processing time but does so at the cost of limiting the fraction of the sky that the array can see. The second approach is to arrange the antennas into a regular, rectangular grid. In this arrangement the necessary computing power rises much more slowly – as Nlog2N – because many of the pair correlations are repeated throughout the grid and so the number of individual calculations can be reduced. However, this arrangement provides a much lower resolution than an array with antennas arranged arbitrarily.

Now, Max Tegmark of the Massachusetts Institute of Technology and Matias Zaldarriaga of the Institute for Advanced Study in Princeton have shown how to achieve high resolutions using affordable computing. The trick is to arrange antennas into hierarchies. For example, as shown in the figure, antennas are arranged into 5×3 blocks, which are themselves arranged into 3×3 blocks, and these then placed within a still larger 3×3 block. Tegmark and Zaldarriaga found that a slightly expanded version of the same algorithm used to correlate pairs of antenna outputs in a rectangular grid could also be used to process the data in such a hierarchical layout. The result is a significant improvement on the resolution of a simple grid while preserving the Nlog2N relationship.

Much less computing power

Tegmark points out the cost implications for a radio telescope with a total surface area of 1 km2, as the proposed Square Kilometre Array (SKA) would have. Assuming that such a telescope consists of a million antennas, each 1 m2 of an Nlog2N arrangement would require 25,000 times less computing power than a conventional N2 layout. "This means that, for a lower cost, one can build an even more powerful instrument that observes the whole sky at once, instead of discarding sky information by lumping antennas into tiles," he says.

The pair admits that its hierarchical layouts will limit the beam shapes that telescopes can have because, like any more regular arrangement, there will be more pairs of antennas with identical orientations and therefore fewer unique viewpoints. But they say that this problem will in part be overcome by the rotation of the Earth.

Long gone is the day when science was given blank cheques Max Tegmark, MIT

They also concede that hierarchical layouts can only approximate the geometrical arrangement of antennas desired for some particular observations. On this point, Tegmark asks whether the case for non-hierarchical layouts is compelling enough to justify the extra cost. "Long gone is the day when science was given blank cheques," he says. "So it's very important to see if we can do things more cheaply."

However, Tim Cornwell of the Australia Telescope National Facility in Sydney believes that hierarchical layouts of radio telescopes would have a number of disadvantages that would make them unattractive to astronomers. Chief among these, he says, would be the much longer time it would take to image the whole sky (while waiting for the Earth to rotate), making it very difficult to carry out surveys and monitor transient sources. He adds that the computing costs of all radio telescopes that might be built over the next 10 years won’t be prohibitive.

The work is published on arXiv.