BAUGH: COSMOLOGICAL MODELLING COSMIC COOKERY: THE MOVIE 1 2 1: The opening titles. The images of the solar system were made by Nigel Metcalfe using a program called Celestia, which was written by Chris Laurel. 3(a) 2: Looking back at the disc and centre of the Milky Way. (Sequence courtesy of Robert Patterson and Stuart Levy of the National Centre for Supercomputing Applications at the University of Illinois at Urbana-Champaign, USA) 3: These three images show sce Cosmic cookery: growin Carlton M Baugh describes cosmological modelling – and how to tell the world about it. O ne of the fundamental questions facing cosmologists today is “How are galaxies made?”. Ever since astronomers realized at the start of the last century that the universe contained many billions of galaxies in addition to our own Milky Way, the challenge has been to explain where these vast agglomerations of stars came from. Why do galaxies come in a range of distinct shapes or morphologies, ranging from spheroidal elliptical galaxies to disc-shaped spiral galaxies? Did galaxies form ABSTRACT Understanding how galaxies are made is one of the great unsolved problems in cosmology. Last year, a team from the Institute for Computational Cosmology at Durham University took part in the Royal Society’s Summer Science Exhibition, with a remit to explain the latest research on galaxy formation to the public. The centrepiece of our exhibit was a stereoscopic movie called Cosmic Cookery. Here I recount how the movie takes the audience on a 3-D tour of the universe and back to the Big Bang, explaining our current ideas about how galaxies are built. in a spectacular flurry of star-forming activity back in the early universe or is the process of galaxy formation a more drawn out affair? Why do we not see galaxies that are many orders of magnitude brighter and more massive than the Milky Way? Is there some process that effectively sets an upper limit on their size? Tremendous advances have been made over the past 20 years towards developing a theory of galaxy formation. Through the use of increas- 1: A cosmic A-to-Z Our view of the local universe has been revolutionized over the past decade. The breakthrough was made possible by the development of multi-object spectrographs, that could take spectra of hundreds of galaxies at the same time within a single field of view. This gave astronomers a tremendous multiplex gain over the first redshift surveys carried out in the 1970s (and indeed up to the early 1990s), in which the redshift of only one galaxy could be measured for each exposure and pointing of the telescope. Two surveys have taken advantage of this technological leap: an Anglo-Australian collaboration (subsequently including institutions in the USA), including the ICC, 2.10 called the two-degree field galaxy redshift survey (2dFGRS); and the US-led Sloan Digitial Sky Survey (SDSS). The 2dFGRS was completed in 2002, mapping the positions of more than 221 000 galaxies, 10 times bigger than the largest previous complete survey. The SDSS is ongoing and has now clocked over 600 000 galaxies. A map as large as the 2dFGRS can be analysed in several ways. Members of the ICC have led analyses of the distribution of galaxies to establish how the clustering signal depends upon intrinsic properties such as luminosity and colour, and also to ascertain whether or not galaxies belong to groups or associations within a common dark-matter halo. These analyses give important new constraints on theoretical models of galaxy formation, such as the efficiency with which baryons are turned into stars in haloes of different masses. The distribution of galaxies on very large scales can be readily interpreted in terms of the clustering of the underlying dark matter. Shaun Cole of the ICC led an investigation by the 2dFGRS team into the large-scale clustering of galaxies, as quantified by the power spectrum (Cole et al. 2005). The power spectrum is the Fourier transform of the simplest measurement of clustering, the auto correlation function. The correlation function measures the excess probability, compared with a random A&G • April 2006 • Vol. 47 BAUGH: COSMOLOGICAL MODELLING 3(b) 3(c) nes of flying through one of the largest maps of the universe, the 2dFGRS. (Images made by Nigel Metcalfe, Nick Holliman and the 2dFGRS team) g galaxies in a computer ingly sophisticated computer models, guided by breathtaking observational breakthroughs, a convincing paradigm that explains how galaxies are built is beginning to emerge. An equally daunting proposition is to explain these ideas and results to a general audience. Last year, the Institute for Computational Cosmology (ICC), part of the Department of Physics at Durham University, made a successful application to participate in the Summer Science Exhibition 2005. This event, run by the Royal Society, showcases exciting research from all fields of science for members of the public. Summer Science has its roots in the soirees run by the Society in the late 1800s. The modern event is much more inclusive and is attended annually distribution of galaxies, of finding two galaxies at a given separation. In the gravitational instability paradigm, the power spectrum grows in amplitude as the distribution of matter gets lumpier. On small scales, the shape of the power spectrum can also change with time. Worse still, this distortion in shape could be different for galaxies than for the dark matter. On large scales, however, these complications do not occur. Hence, an accurate measurement of the shape of the power spectrum of galaxies on large scales gives the shape of the power spectrum of the dark matter. Moreover, this spectrum can be related simply to the spectrum of density fluctuations in the early universe. The shape of A&G • April 2006 • Vol. 47 by around 4000 members of the general public, school pupils and dignitaries such as Members of Parliament. Cosmologist for a day The ICC display was called “Cosmic Cookery: Growing Galaxies in a Computer”. Our exhibit had a number of elements, giving visitors the chance to become cosmologists for the day and putting them in control of a computer simulation of a cosmic collision between two spiral galaxies to make a new galaxy, thereby testing ideas about how elliptical galaxies are made. The focus of the exhibit was a stereoscopic movie which, as we shall see below, started with a tour of the universe before explaining how we the spectrum at this epoch depends on basic cosmological parameters, such as the fraction of matter that is in the form of baryons and the density of matter in units of the critical density (i.e. the density required to give the universe a flat geometry). In particular, the presence of baryons in the matter budget of the universe leaves a characteristic oscillatory signature in the power spectrum which was evident in the 2dFGRS measurement. Recently, we combined the 2dFGRS measurement of the power spectrum of galaxies with a compilation of the latest measurements of the temperature anisotropies in the microwave background radiation (Sanchez et al. 2006). think galaxies are made. The movie took around six months to compile, using a combination of images generated from observational data and from computer simulations. Providing the viewer with a stereoscopic or 3-D view of the universe was an essential feature of the movie; the stereoscopic animations were generated by the the e-Science Research Laboratory at Durham University, led by Nick Holliman. Holliman’s group attained 3-D effects by producing slightly offset images in linearly polarized light. The images were projected onto a screen and viewed with glasses fitted with filters. These glasses looked as if they came from the movie Top Gun and were a big hit with the younger members of the audience. These two observables depend upon the basic cosmological parameters in different ways, so using them in combination can significantly tighten the constraints on some parameters. The best fitting cold dark matter model is shown by the solid line in figure 9. Here we have plotted the power spectrum of galaxies (blue symbols) and the spectrum of temperature fluctuations in the microwave background on the same axes. It is a remarkable vindication of the cold dark matter model that these two observations, measuring the properties of the universe separated in time by nearly 14 billion years, are in such spectacular agreement with the theoretical prediction. 2.11 BAUGH: COSMOLOGICAL MODELLING COSMIC COOKERY: THE MOVIE 4(a) 4(b) 5 4: The Millennium Simulation. Brighter colours indicate higher densities of dark matter. (Images by Volker Springel, John Helly and the Virgo Consortium) The collaboration with the e-Science group is continuing and is becoming increasingly valuable for research, as well as for making animations for outreach activities. Modern simulations and astronomical observations produce huge datasets that are difficult to manipulate by traditional methods. The visualization of these huge datasets literally gives the researcher a new view of the subject and will be invaluable in aiding the development of new analysis techniques and methodologies. The production of the stereoscopic animations for the Cosmic Cookery movie also presented new challenges for Holliman and his team; their experiences have been written up in a research paper that was presented at a meeting on Stereoscopic Displays and Applications in the US in January this year (Holliman et al. 2006). Whistle-stop tour of the solar system Here we take the reader on a scene-by-scene run through of Cosmic Cookery. We give a brief storyline and state the origin of the images used in each segment. Certain sequences show results of research that was either carried out at the ICC or in which members of the ICC have played a major role; these results are dealt with in more detail in the boxes. The movie starts with an invitation to the audience to take a flight through the universe in an “impossibly fast” spaceship. The voyage begins, appropriately, at the Earth (figure 1). The camera then moves swiftly through the solar system, pausing to marvel at the giant red spot of Jupiter and the rings and moons of Saturn. The solar system sequence was created by Nigel Metcalfe using software called Celestia, which was written by Chris Laurel. This software is used by planetariums and can be downloaded free of charge from http://www.shatters .net/celestia. Celestia can be used to produce an animation by specifying a flight path and outputting a sequence of still images along the path. However, Celestia does not produce stereo output, and so left and right viewpoints had to be captured separately and combined to produce a stereoscopic view of the solar system. Leaving the Milky Way A key aim of the opening sequences was to convey to the non-specialist the relative scale of different astronomical objects and to illustrate what a galaxy is and how they are distributed in 5: The pattern of temperature ri background radiation.(Image co Microwave Anisotropy Probe [W the universe. After leaving the solar system behind, we soon emerge from the disc of the Milky Way, glimpsing a spectacular view of our galaxy as we look back towards the galactic centre (figure 2). We then pass the Magellanic Clouds, before moving towards the Virgo Cluster with M87 at its centre. The images for this sequence were provided by Robert Patterson and Stuart Levy from the National Centre for Supercomputing Applications at the University of Illinois at Urbana-Champaign, USA. The software used to produce the images is a 3-D visualization tool called Partiview, developed by Stuart Levy. This software is being used by the Hayden Planetarium, part of the American Museum of Natural History, in their Digital Universe exhibit and also featured in a recent television documentary. Our cosmic back yard We continue our journey out into the local universe, flying through a map of our cosmic neighbourhood, the two-degree Field Galaxy Redshift Survey (2dFGRS, see box 1). This survey looks out in two directions in the sky and so has two parts shaped like pie wedges. We fly through one wedge, starting at the apex, before 2: The Millennium Simulation: a computer model of the universe Numerical simulations have been instrumental in driving many of the advances in theoretical cosmology over the past 20 years. The cold dark matter model is particularly amenable to computer modelling. First, the initial conditions for the calculation are encoded in the cosmic microwave background radiation. Secondly, the dark-matter particles only interact through gravity; fast algorithms exist for computing the long-range gravitational forces between particles. Finally, the dark matter is cold, which 2.12 means that the small scale, thermal motions of the particles can be ignored, unlike in the case of massive neutrinos, a one-time candidate for the dark matter, which was referred to as hot dark matter. As computing power has ramped up according to Moore’s Law, the number of particles used to represent the cold dark matter in simulations has also increased, with the biggest simulation of the day following a relation similar to the curve quantifying the increase in CPU speed. Last year, the Virgo Consortium for Cosmological Simulations, an international collaboration between institutions in Germany, the UK (including the ICC, the UK base of the Virgo Consortium), Canada, the USA and Japan, reported on a calculation called the Millennium Simulation, which was ahead of its time in that it actually jumped off the simulation version of Moore’s Law. The first results from the simulation were published in Nature, with an image of the dark matter in the simulation A&G • April 2006 • Vol. 47 BAUGH: COSMOLOGICAL MODELLING 6(a) pples in the cosmic microwave urtesy of the Wilkinson MAP] science team and NASA) 6(b) 6: A high-resolution simulation of the formation of a dark matter halo. (a): A snapshot at an early time in the simulation. (b): The halo at the present day. (Images courtesy of Adrian Jenkins and Nick Holliman) panning out to look back at the filamentary structure traced out by the galaxies, which is sometimes referred to as the “cosmic web” (figures 3a,b,c). This sequence was produced in Durham by Nigel Metcalfe and Nick Holliman. The galaxy images are high-quality snapshots of a small sample of nearby galaxies, collated from the archives of various telescopes. An image is then assigned to a 2dFGRS galaxy on the basis of its colour, i.e. redder galaxies in the 2dFGRS are matched to an image of an elliptical galaxy. The size of the image depends upon the absolute luminosity of the galaxy. A computer-generated universe Now that we have seen the lumpy distribution of galaxies in the 2dFGRS, we can ask if computer-generated universes look anything like the real thing. Figures 4a and 4b show stills from a fly-through of the Millennium Simulation, an enormous calculation carried out by the Virgo Consortium for Cosmological Simulations (described in more detail in box 2). The simulation tracks the growth of structure in the dark matter, as gravity acts so that tiny ripples in the density of matter in the early universe grow in size. The sequence starts with a global view of appearing on the front cover (Springel et al. 2005). The Millennium Simulation used more than 10 billion particles to model the dark matter in a volume bigger than that sampled by the 2dFGRS or SDSS maps. The calculation ran for 28 days on a 512-processor supercomputer belonging to the Max Planck Society in Germany, clocking up 343 000 processor hours. The output from the simulation takes up more than 25 Tb of disc space. Despite the large volume covered by the A&G • April 2006 • Vol. 47 the simulation at the present day, which shows that the dark matter traces out a filamentary pattern bearing a striking resemblance to the 2dFGRS galaxy map. The camera then zooms into one of the biggest dark-matter haloes in the Millennium Simulation, which is equivalent in size to a cluster of galaxies bigger than the Virgo Cluster. The images for the Millennium Simulation fly-through were generated by Volker Springel of the Max Planck Institut für Astrophysik at Garching, Germany, and by John Helly of the ICC. The origin of cosmic structure Where did the structures we see in the Millennium Simulation come from? In the current paradigm, the structures have a quantum origin; fluctuations in the density of the universe on microscopic quantum scales are thought to have been boosted to classical scales during a period of extremely rapid expansion of the universe called inflation. In the Big Bang cosmology, the early universe was much denser and hotter than it is today. Matter was therefore in the form of an ionized plasma and the free electrons coupled strongly with the photons. Variations in the strength of the gravitational calculation, the huge number of particles employed means that dark-matter haloes as small as those thought to host the Large and Small Magellanic Clouds, small neighbours of the Milky Way, can be resolved in this simulation. This unprecedented resolution in a cosmologically representative volume makes the simulation an ideal test-bed for models of galaxy formation. The simulation contains around 20 million dark-matter haloes and so can resolve between 50 and 100 million galaxies. Running potential due to density fluctuations were reflected by changes in the temperature of the radiation. As the universe expanded, the pressure and temperature fell and the plasma became a neutral gas of atoms leaving few electrons to interact with the radiation. The density fluctuations present in the universe at this time, the epoch of recombination, are fossilized in temperature anisotropies in the cosmic background radiation. The cooling of the radiation caused by the subsequent expansion of the universe means that this radiation is seen today as feeble microwaves. The cosmic microwave background radiation is dappled with hot and cold spots, which reflect the fluctuations in the density of matter in the universe around 400 000 years after the Big Bang (figure 5). The cradles of galaxy formation The pattern of hot and cold spots seen in the microwave background provides the initial conditions for computer simulations of structure formation in the universe. The next sequence shows an ultra-high-resolution simulation concentrating on the formation of a single dark-matter halo. At an early time, the matter that ends up in the halo is split into less models of galaxy formation on such a scale presents a new set of computational challenges. Nevertheless, the first calculations of the properties of galaxies expected in the Millennium Simulation universe have recently appeared (Croton et al. 2006, de Lucia et al. 2006, Bower et al. 2006). This new generation of galaxy-formation models suggests that the growth of supermassive black holes found in galactic spheroids is intimately linked to the growth of the galaxy hosting the black hole. 2.13 BAUGH: COSMOLOGICAL MODELLING COSMIC COOKERY: THE MOVIE 7: A synthetic galaxy generated using a computer model that tracks the evolution of the baryons and the dark matter. (Image by Takashi Okamoto, Richard Bower, Adrian Jenkins, Nigel Metcalfe and Nick Holliman) massive progenitors, as shown in figure 6a, the first still. The distribution of dark matter is quite stringy and filamentary. The force of gravity, acting over billions of years, brings these fragments together and the halo builds up as smaller haloes merge together. The second still, figure 6b, shows the halo at the present day. Yellow indicates a higher density of matter. The final structure is more spherical. A few highdensity lumps can be seen within the larger halo. These are called substructures and correspond to the cores of the ancestors of the final halo. The more diffuse outer regions of these progenitor haloes have been stripped off during the merger process. Only the high-density central regions of the progenitors retain their identity after merging with a more massive 8: A real galaxy and a computer model side by side. Can you tell which one is which? (Image by Takashi Okamoto, Richard Bower, Adrian Jenkins, Nigel Metcalfe and Nick Holliman) structure. Cosmologists believe that galaxies grow within dark-matter haloes. Growing a galaxy in a computer Next we rewind the computer simulation back to the initial conditions and repeat the calculation again, but this time we include baryons as well as dark matter. This new calculation is much more difficult to carry out. In addition to the force of gravity, the baryons are subject to other forces and phenomena such as star formation that in many cases are poorly understood (see box 3 for more details). One of the long-standing problems in numerical galaxy formation has been to produce discs that resemble observed spiral galaxies. It turns out, as explained in box 3, that the morphology of a galaxy depends sensitively on the construction history of the dark matter halo and the way in which the astrophysics of galaxy formation are modelled. A model disc galaxy like that shown in figure 7 took a lot of tinkering with the recipe to get the mix of ingredients just right. Is the computed galaxy realistic? The final sequence of Cosmic Cookery starts by comparing the galaxy grown in the computer with a real galaxy (figure 8). The real image has been processed in the same way as the computer galaxy, and shows stars and cold gas. The simulated galaxy disc has a very similar size and structure to the real one. This gives theoreticians some encouragement that they are on the right path to understanding how galaxies are made. 3: Growing a galaxy in a computer The focus in computational cosmology is shifting firmly towards understanding the formation of galaxies. This is a much more challenging problem than following the growth of structure in the dark matter, because a much wider range of phenomena have to be considered. Quite often, these processes are nonlinear and the underlying physics is poorly understood. The spatial resolution required to follow the formation of galaxies is more demanding than that needed for the dark matter alone; typically, the scale-size of a galaxy is 10 times smaller than the radius of its dark-matter halo. The current paradigm for galaxy formation is that dark-matter haloes act as the cradles in which galaxies grow. The dark haloes are built up as density fluctuations grow through gravitational instability, with overdense regions accreting matter. The baryons initially trace the distribution of the dark matter and get heated up when the dark matter collapses to form a self- 2.14 gravitating lump or halo. Unlike the dark matter, the hot baryons can lose energy by radiation. The baryons cool down when they lose energy on radiating away photons, and the corresponding drop in pressure causes the baryons to shrink towards the central parts of the halo, forming a disc that retains a non-zero size because it is rotating. The exact size of the cold gas disc that results depends upon the conservation of the angular momentum of the gas, as we shall see. Once there is a supply of cold gas, the gas is turned into stars. In the absence of a theory for star formation, modellers resort to using a recipe or rule to describe the rate at which cold gas is transformed into stars. Such a recipe contains parameters whose values are set so that the model reproduces a particular observational result. Once stars have formed, those above eight solar masses undergo a supernova explosion, depositing energy and metals in the interstellar medium. This can have an impact on the subsequent rate of star formation, if the energy from the supernova heats up some of the cold gas and moves it from the disc. The class of models developed to follow the processes thought to be important for galaxy formation are called semi-analytical galaxy formation models. These are ab initio calculations that start from primordial density fluctuations and follow the growth of dark-matter haloes, the heating and cooling of gas, star formation and events such as supernova explosions, which are called feedback processes. In addition, the models can trace mergers between galaxies and track the stellar populations of the model galaxies to generate synthetic spectra. One particularly challenging problem that the models have faced recently was to explain the discovery of a population of galaxies at high redshift seen only by emission from the dust they contain, which is detected at sub-millimetre wavelengths (Smail et al. 1997, Blain et al. 2002). A&G • April 2006 • Vol. 47 BAUGH: COSMOLOGICAL MODELLING Preparing the Cosmic Cookery exhibit took around six months, involving staff from the ICC, the Durham e-Science Research Laboratory and the Electrical and Mechanical Workshops of the Department of Physics at Durham. Phil Brown of Media 55 Ltd carried out the production of the movie, with Nick Holliman, delivering the final copy the weekend that we left for London! Many organizations contributed directly and indirectly towards the cost of mounting the exhibit, including PPARC, the Royal Society, the de Laszlo Foundation, Inition Ltd, the RAS and the National Centre for Supercomputing Applications in the USA. After a hectic day setting up the Cosmic Cookery stand, under the command of the ever-resourceful and indispensable Lydia Heck, we were ready for the public. At this point the demonstrators, a mixture of postgraduates and staff, actually began to enjoy themselves. They found that explaining their research work to an enthusiastic and genuinely interested public was a rewarding experience. The Cosmic Cookery exhibit is on permanent display in the Ogden Centre for Fundamental Physics at Durham. It is used on university open days and in the annual Durham University Science Festival. The Odgen Centre (which comprises the ICC and the Institute for Particle Physics Phenomenology) has a vigorous outreach programme, part-funded by PPARC and run by Dr Pete Edwards. As part of this work, there are numerous visits to the Ogden Centre each year by school parties, who get to see Cosmic Cookery. To date, the programme has reached more than 6000 school children of all ages in the Northeast. Elements of the Cosmic An exhaustive search through the parameter space of the models did not yield a solution that could explain both the galaxies seen at high redshift and the properties of galaxies in the local universe. In an act of desperation, we tried a model in which the initial mass function (IMF) with which stars are produced in bursts is flat. This means that the same proportion of stars of all masses are made in bursts, rather than the case with quiescent or steady star formation in discs, for which we use a standard choice of IMF, which is biased in favour of low-mass stars. These bursts of star formation are triggered in the models by certain types of mergers between galaxies. By favouring high-mass stars in bursts, more metals and more ultraviolet light are generated. Shorter wavelengths are better absorbed by dust, so more energy goes into heating the dust. However, the higher yield of metals means there is also more dust. These two effects combined boost the flux from the model A&G • April 2006 • Vol. 47 9: The fluctuations in the cosmic microwave background, as measured by WMAP, plotted in the same units as the power spectrum of galaxies in the 2dFGRS. The solid line shows the best-fitting cold dark matter model. (Image by Ariel Sanchez) 104 P(k)/(h–1 Mpc)3 What next for Cosmic Cookery? 103 WMAP 2dFGRS 0.001 0.01 k/(h Mpc–1) Cookery movie will be seen this year by around 10 000 school children across the UK, as Dr Edwards is delivering the Institute of Physics Schools and Colleges Lecture “Gravity, Gas and Stardust” in 2006. We also hope to take the Cosmic Cookery display to different venues across the Northeast. Initiatives like the Ogden Centre outreach programme and Cosmic Cookery should prove to be invaluable resources in efforts to reverse the trend of declining numbers of pupils taking A-level physics. ● galaxy at submillimetre wavelengths. This controversial change to the IMF resulted in a model that could reproduce the distribution of galaxies in the universe at both high and low redshifts (Baugh et al. 2005). Support for a non-universal IMF also came from a numerical simulation of the formation of an individual galaxy (Okamoto et al. 2005). A long standing problem in numerical simulations has been to form a disc-like galaxy that has the same size as observed spiral galaxies. The simulations tend to make galaxies that are an order of magnitude too small and look more like ellipticals than spirals. Part of the problem is that gas tends to cool early on in the simulations, forming small clumps that merge together to make larger galaxies. During the merging process, the clumps of cold gas and stars tend to give up their angular momentum, transferring the spin to the outer parts of the dark halo. Thus the resulting disc contains too little angular 0.1 C M Baugh, Institute for Computational Cosmology, Dept of Physics, Durham University, UK. References Baugh C M et al. 2005 MNRAS 356 1191–1200. Blain A W et al. 2002 Physics Reports 369 111–176. Bower R G et al. 2006 astro-ph/0511338. Cole S et al. 2005 MNRAS 362 505–534. Croton D et al. 2006 MNRAS 365 11–28. de Lucia G et al. 2005 astro-ph/0509725. Holliman N et al. 2006 SPIE 6055A in press. Okamoto T et al. 2005 MNRAS 363 1299–1314. Sanchez A G et al. 2006 MNRAS in press. Smail I et al. 1997 ApJ 490 L5. Springel V et al. 2005 Nature 435 629–636. momentum and is much smaller than real spiral discs. Okamoto et al. found that if they also adopted a top-heavy stellar IMF in starbursts, the higher number of supernova explosions that result from forming more high-mass stars means that much less gas cools down in small clumps at early times. The baryons tend to stay in the hot phase and cool at a later stage in the evolution of the galaxy. By cooling later on, more of the angular momentum of the gas is retained and a beautiful disc galaxy results (see figures 7 and 8). There is one note of caution. A spiral galaxy is rather like a soufflé: the astrophysical conditions have to be just right or this experiment in cosmic cookery turns out all wrong. The morphology of the galaxy is sensitive to the way in which the star formation and the associated feedback from supernova explosions are modelled. Nevertheless, this calculation represents an encouraging step towards understanding how galaxies like our Milky Way were made. 2.15
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