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mechanism in systems with heterogeneous connectivity patterns, is just such an investigation. And an important one at that — the Turing mechanism7,8 represents a classical model for the formation of self-organized spatial structures in non-equilibrium systems. In its simplest setting, Turing patterns can develop in reaction–diffusion systems, in which an activator enhances its own production while an inhibitor suppresses the activator. In 1952, Alan Turing showed that such an activator–inhibitor system can be destabilized when the inhibitor is more mobile than the activator8. This diffusion-driven dynamical instability leads then to the development of stable spatial patterns, formed by activator-rich and activator-depleted regions. Applications of the Turing mechanism reach from ecology to developmental morphogenesis, where it has been proposed as an explanation of the development of the pigment patterns in animals9 (Fig. 1).
In their study, Nakao and Mikhailov2 consider a specific example of an activator–inhibitor system, known as the Mimura–Murray ecological model. They place this model on top of heterogeneous networks and perform a linear stability analysis, which reveals the presence of the Turing instability for a given ratio of the diffusive constants of the activator and inhibitor. However, the instability is not, as one might expect and as other models assume, localized in the
hubs (that is, in the most connected nodes of the network), but in a set of vertices in which the degree of connectivity is inversely proportional to the characteristic scale of diffusion. The segregation leading to the Turing patterns therefore takes place mainly in vertices with a low number of connections. The process proceeds by a differentiation of vertices with high and low concentration of activator, until a steady-state, stable pattern is achieved, leaving behind a non-homogeneous distribution of activator and inhibitor throughout the network.
Whereas Nakao and Mikhailov2 do not provide any direct experimental evidence of their model, the study of Turing patterns in complex networks has potential practical applications in the field of theoretical biology. The reactions taking place at the early stages of development can be modelled more accurately using a network as a substrate, instead of a continuous parameter space. A handle on Turing patterns in networks may thus lead to a fuller understanding of basic issues in morphogenesis and early development. Furthermore, reaction–diffusion systems are also capable of describing the evolution of populations in an ecological environment, and the Turing mechanism could provide an understanding of the diverse distribution of species in ecological niches. Given that biological ecosystems can be most naturally
represented in terms of complex networks, the work of Nakao and Mikhailov should open the path to new insight into this fascinating issue, as well as to the possible development of controlled experiments capable of checking the validity of their results. ❐
Romualdo Pastor-Satorras is in the Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, c. Jordi Girona 1–3, 08034 Barcelona, Spain; Alessandro Vespignani is at the Center for Complex Networks and Systems Research, School of Informatics and Computing, and the Pervasive Technology Institute, Indiana University, 107 South Indiana Avenue, Bloomington, Indiana 47406, USA, and at the ISI Foundation, Viale S. Severo 65, 10133 Turin, Italy. e-mail: [email protected]; [email protected]
References1. Barrat, A., Barthélemy, M. & Vespignani, A. Dynamical Processes
on Complex Networks (Cambridge Univ. Press, 2008).2. Nakao, H. & Mikhailov, A. S. Nature Phys. 6, 544–550 (2010).3. Albert, R. & Barabási, A-L. Rev. Mod. Phys. 74, 47–97 (2002).4. Dorogovtsev, S. N. & Mendes, J. F. F. Evolution of Networks
(Oxford Univ. Press, 2003).5. Pastor-Satorras, R. & Vespignani, A. Evolution and Structure of the
Internet (Cambridge Univ. Press, 2004).6. Newman, M., Barabási, A-L. & Watts, D. J. The Structure and
Dynamics of Networks (Princeton Univ. Press, 2006).7. Murray, J. D. Mathematical Biology II: Spatial Models and
Biomedical Applications (Springer, 2003).8. Turing, A. M. Phil. Trans. R. Soc. Lond. B 327, 37–72 (1952).9. Murray, J. D. Sci. Am. 258, 80–87 (March 1988).
Galaxy clusters are the largest objects in the Universe, and contain the largest galaxies and black holes. Only 3% of
the mass of galaxy clusters is in the familiar form of stars, however: the majority (84%) is composed of dark matter, and the remaining component is a hot dilute plasma, known as the intracluster medium or ICM, that emits copiously at X-ray wavelengths. Yet despite their size and importance in the pantheon of cosmological objects, galaxy clusters still hold many mysteries. In particular, the interplay of heating and cooling in the clusters is poorly understood, as is the role of magnetic fields.
In astronomy, magnetic fields are one of the trickiest things to measure. Yet, as they report in Nature Physics,
Christoph Pfrommer and Jonathan Dursi1 have succeeded in making the first measurements of the orientation of magnetic fields in a galaxy cluster, for the nearby Virgo galaxy cluster. As well as being a measurement first, their technique — using computational simulations to complement observations — is a promising direction for progress in astrophysics.
Why do we care about magnetic fields in galaxy clusters? A major unsolved problem lurks near the centres of these objects, where the cooling time in the 5,000,000 K X-ray-emitting plasma is 100–1,000 times shorter than the age of the galaxy clusters. This would not be an issue except that we don’t observe any gas cooling below
1,000,000 K (ref. 2). Therefore, something must be heating the ICM to prevent what is known as a cooling catastrophe, or cooling flow, from occurring. The two most obvious possibilities are black-hole feedback through energetic jets and bubbles, or thermal conduction from the hot plasma outside the core. The plasma is strongly magnetized and magnetic fields are amazing conduits of heat, having high thermal conductivity along magnetic field lines and nearly perfect insulation across magnetic field lines — but this means we need to know the magnetic geometry to assess the efficacy of heating by thermal conduction.
Magnetic fields, however, are notoriously difficult to measure remotely in space.
AsTROPhYsICs
Magnetic bubble wrapThe orientation of the magnetic field wrapped around a galaxy cluster has been measured for the first time, through a previously unexplored combination of traditional astronomy and computer simulations.
Ian Parrish
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Several techniques have previously been used to measure the integrated magnetic-fi eld magnitude, but never the orientation of a fi eld in the ICM3. Yet galaxy clusters, aft er all, contain a lot of galaxies (as well as dark matter and the ICM), so Pfrommer and Dursi have used observations of these galaxies running into the ambient plasma to determine the magnetic fi eld. Th e galaxies sweep up ambient ICM magnetic fi eld as they orbit in the cluster, such that the fi eld becomes ‘draped’ around the galaxy clusters. Th is draped magnetic fi eld has been dubbed “bubble wrap for bullets”, as it insulates the galaxies from the surrounding cluster gas and prevents instabilities from mixing the galaxy with its surroundings4. Meanwhile, observations of the polarized radio emission in the galaxies themselves have revealed the orientation of the galactic magnetic fi eld (although this technique does not work in the dilute ICM)5. Pfrommer and Dursi1 have correlated the draping eff ect with these measured galactic magnetic fi elds to extract the orientation of the swept-up magnetic fi elds.
Th e scientifi c method used here would be unrecognizable to your eighth-grade science teacher. For example, to measure the gravitational acceleration, g, in a lab on Earth, you could drop weights from various heights and time their falls, quickly discovering that g ≈ 9.8 m s−2. Now imagine that you had to
determine the strength of gravity by looking at various snapshots of falling weights — a much harder task. Th is is how the Universe presents data to us. Instead of formulating and testing a hypothesis using repeatable experiments, in astronomy it’s necessary to synthesize a variety of observations at a fi xed time.
Pfrommer and Dursi have in eff ect performed a series of experiments, using numerical simulations based on magnetohydrodynamics. Th e novelty is that they simulated a set of galaxies being draped by the ICM and then used these sets of simulations as a calibration for understanding observational data. In the absence of the numerical study, there would be no way to connect observations of the magnetic fi eld in the galaxies to the orientation of the magnetic fi eld in the ambient ICM. A major caveat is in order here, however, as it is always diffi cult to be certain that the physics contained in the simulation captures all the important physical processes present in nature. But, as computers become more powerful, we should expect to see the interplay of theory, simulation and observations become far more prevalent.
For galaxy clusters, this cycle of discovery has now come full circle. It was shown several years ago that the so-called magnetothermal instability would operate in
the outer parts of galaxy clusters6. Numerical simulations predicted that this instability would saturate by reorienting the magnetic fi eld to be preferentially radial7: Pfrommer and Dursi’s work seems to confi rm that the magnetic fi elds indeed seem to be radially aligned in the Virgo cluster. Next there is the exciting prospect of extending their technique to the study of the geometry of magnetic fi elds in the central regions of clusters, where the cooling time is short, and making the fi rst measurements that show how thermal conduction could potentially solve the cooling fl ow problem at the heart of galaxy clusters. ❐
Ian Parrish is in the Department of Astronomy, University of California at Berkeley, Berkeley, California 94720, USA.e-mail: [email protected]
References1. Pfrommer, C. & Dursi, L. J. Nature Phys.
6, 520-526 (2010).2. Peterson, J. R. & Fabian, A. C. Phys. Rep. 427, 1–39 (2006).3. Carilli, C. L. & Taylor, G. B. Ann. Rev. Astron. Astrophys.
40, 319–348 (2002).4. Dursi, L. J. Astrophys. J. 670, 221–230 (2007).5. Wezgowiec, M. et al. Astron. Astrophys. 471, 93–102 (2007).6. Balbus, S. A. Astrophys. J. 534, 420–427 (2000).7. Parrish, I. J., Stone, J. M. & Lemaster, N. Astrophys. J.
688, 905–917 (2008).
Published online: 16 May 2010
To improve resolution, individual telescopes can be arranged into an array of telescopes. By means of interferometry the telescopes are then able to reach resolutions equivalent to that of a single enormous dish. At present, the largest such array is the Low Frequency Array (LOFAR). It is under construction across Europe and instead of individual telescopes — which would have to be very large to be sensitive to the long wavelengths measured — it employs array stations consisting of many low-cost antennas.
The fi gures illustrate the eff ect of long-baseline interferometry. With fi ve stations spread across the Netherlands, the quasar 3C 196 looks like a featureless blob in the 4–10-m-wavelength range (left). Now add three stations in Germany, the farthest being near Munich: suddenly the resolution improves tenfold and details emerge (right); in fact, the image on the right zooms into the central region
More stations tune inRADIO AsTRONOMY
of the quasar, so the actual diff erence between the two images is a factor of 40. The quasar is a strong radio emitter, but even so, it is 7 billion light-years away.
LOFAR will soon include other stations, not to mention shorter-wavelength data,
to further improve the resolution. In addition to probing mysteries of the early Universe, it will also have geophysical and agricultural applications.
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