Imagine you could time travel to decades after the first detections of gravitational waves by ground-based interferometers: someone has already had the call from Stockholm, a series of amazing gravitational wave discoveries have been reported and the watching world is going wild about gravitational wave astronomy. Such momentous events would certainly trigger the demand for even more sensitive and powerful gravitational wave detectors to drive forward this exciting new field of observational astronomy. But the immediate question would be: where to put these multi-billion dollar instruments? Future generations of gravitational wave detectors, like the proposed European Einstein Telescope, would be very expensive to build, so choosing the most favourable sites in which to build them will be a crucial issue. Our work, published in Classical and Quantum Gravity, explores the question of where we should build these huge machines, in order to maximise their scientific output.
There are numerous issues that might prevent us from placing a detector at a specific site. It is completely impractical to build a gravitational wave detector underwater, for example, which essentially excludes any oceans, seas and fresh water locations. We can expand our list of ‘exclusion regions’ to include many other factors, such as coastlines, seismically active zones, major roads and populated areas, all of which would generate excessive environmental disturbances; polar regions, elevated areas and slopes that would demand prohibitive extra effort to construct and to maintain; protected areas or military zones which would also be inaccessible. In this way, by using some public databases, we have developed a new perspective on the world map, presenting the ‘allowable’ regions (shown in black on the map above) for building gravitational wave detectors.
Does our gravitational wave world map reveal the best sites for future detectors? Not yet! Before we can provide an answer, first we need to examine more closely the question. We need to properly define what we mean by a “good” detector site. If we were considering only one detector then after removing all of the exclusion zones there is really no single site that is favoured over any other. However, to localise the position of a source on the sky from gravitational wave data alone is made possible using separated detectors – exploiting the tiny differences in arrival time of the gravitational waves at the different sites. So a network of multiple detectors is not merely icing on the cake, but rather something indispensable. This means the performance of a detector network should be considered as a whole, instead of simply assessing its individual components. Following our previous study (published in Class. Quantum Grav. 30 155004) we define the “goodness”, or Figure of Merit, of a network as a balanced combination of performance in relation to three factors: the network’s ability to reconstruct the polarisation of the source, to determine the source’s location on the sky and to estimate the source’s parameters. These factors reflect many of the scientific motivations for gravitational wave astronomy: searching for unknown sources, following up observations with traditional electromagnetic telescopes and studying the astrophysics of the sources themselves. Consequently a good network of gravitational wave detectors would ideally display good performance in all three factors.
We are half way towards the final answer! Imagine that we have finally decided ideal sites for a network of detectors. Suppose we move the entire network a certain distance in some direction; so long as none of the sites stray into the exclusion zones, the shifted network should be just as good as the original one. So again there’s no single best network that intrinsically outperforms all others. This reflects the fact that our definition of performance for a network is based on the relative configuration of the sites instead of their actual locations. In order to distinguish a particular location from the others, some other indicator is needed, and we choose that to be the so-called “flexibility index” – which measures how many different “good” network configurations a particular site could belong to. A site with a high flexibility index would, therefore, be less sensitive to changes in the ‘global’ plan for extending the gravitational wave detector network – e.g. in the event that some other components of an anticipated network were suddenly rendered unsuitable, and “plan A” had to be replaced by “plan B”, or “plan C” and so on. In the previous study a network of two detectors was considered and (according to the figure of merit we defined) two detectors separated by about 130 degrees was found to be ideal. By that definition, Australia hosts the most flexible sites as the 130 degree circle mostly crosses allowable regions. East Asia and North Africa were less favourable, on the other hand, as the 130 degree circle mostly falls in excluded regions.
The situation gets more complicated with more detectors, as the problem’s complexity increases exponentially with the number of detectors. Consequently the exhaustive search method adopted by our previous study is no longer feasible. Approaching the problem from another perspective, we noted that any given detector network can be described by a set of parameters like the sites’ geographical coordinates, which can then be translated into a single number describing the “goodness” of the network as a whole. We want to find those networks which maximise this overall measure of goodness; this resembles closely problems confronted in Bayesian inference, where one must explore and characterise an unknown probability distribution over a high-dimensional parameter space. What’s more, our effective probability distribution, or “posterior”, should be intrinsically multi-modal since the world is divided into continents and these naturally constrain the locations of the multiple modes in the “posterior”. We can therefore apply a novel Bayesian inference method named “mixed MCMC (Markov chain Monte Carlo)”, previously developed for exploring multi-modal posteriors, which is ideally suited to our interesting geographical optimisation problem.
Returning, then, to the original question: where are the best locations to build future generation gravitational wave detectors? We now have the numerical tools to provide an answer! In our paper we performed two case studies: one for a network with three component detectors, and another for a five-detector network. For a three-detector-network, Northern Europe performs as well as Australia as a host region with the most flexible sites, while East Asia and North Africa are not so well placed; these results are consistent with our previous two-detector study. However, for the case of a five-detector-network, we see that almost all allowable regions can host some good networks, although Australia hosts by far the most outstanding sites as measured by their greater flexibility. The figures above show maps of the flexibility index for our three- and five-detector network analyses.
So, for those future committees and funding agencies, who may be charged with planning the next big steps in gravitational wave astronomy, we hope that our study (quite literally!) maps out that exciting future.
Read the full article in Classical and Quantum Gravity:
Global optimization for future gravitational wave detector sites
Yi-Ming Hu, Péter Raffai, László Gondán, Ik Siong Heng, Nándor Kelecsényi, Martin Hendry, Zsuzsa Márka and Szabolcs Márka
Yi-Ming Hu et al 2015 Class. Quantum Grav. 32 105010
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