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UMD ASTR 680 - Clusters: Context and Background

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Clusters: Context and BackgroundWe’re about to embark on a subject rather different from what we’ve treated before,so it is useful to step back and think again about what we want to accomplish in thiscourse. We have been accumulating a set of tools with which we can approach problems inhigh-energy astrophysics. For a given situation we should be able to ask some fundamentalquestions about the reliability of the answers. For example, if we read a paper about blackholes we should ask “will general relativity be import ant”? If so, do the authors applyit correctly? Ask class: what are a couple of questions one might, similarly, ask aboutneutron stars? For neutron stars we can also ask about GR, and also ask whether strongmagnetic fields may play a role. This means that if we see a paper about merging neutronstars that treats gravity in the Newtonian limit, we should be suspicious about the results.Development of physical insight is improved if we consider a variety of physical regimes.In this course we’ve thought about extremely high densities and strong magnetic fields,which are not in the normal run of environments considered even in astrophysics. In thesame spirit of broadening our exposure to different regimes, we will consid er in the nextthree lectures a very different environment, yet one that also has been illuminated greatlyby high-energy observations. This is the subject of clusters of galaxies. Clusters havegreat importance in a variety of contexts, but especially as probes of cosmology and of theformation of the first structure in the universe. This will t herefore bring in many topicsand questions that we have not yet considered. In this lecture we’ll think primarily aboutcontext, in the next lecture we’ll talk about the observational properties and what theyimply, and in the third lecture we’ll talk in detail about the Sunyaev-Zeldovich effect, whichis a growth field that has many cosmological applications.Quick review of propertiesBefore heading into the context, here’s a quick summary of some of the propertiesof clusters of galaxies. Clusters were first catalogued in a systematic way by Abell in1958. He identified some 1700 clusters on the Palomar Observatory Sky Survey plates,by eye, and produced a richness criterion based on the galaxy count within a radius of1.5 h−1Mpc, where h = H0/100 km s−1Mpc−1≈ 0.7. Such a volume typically contains∼ 103galaxies, has a mass M ∼ 1014−15M⊙, a temperature T ∼ 108K, and a total(bolometric) luminosity L ∼ 1043−45erg s−1. The number density of clusters in the localuniverse is about ncl≈ 10−5h3Mpc−3. Approximately 10% of galaxies are in clusters, therest being “field” galaxies. Although “clusters of galaxies” were first discovered optically, bythe, well, clustering of galaxies, galaxies comprise a small fraction of the total mass; mostof the mass is actually dark matter (i.e., a collisionless component that is not specificallyidentified), and most of the rest is in hot gas spread throughout the cluster. It is worthkeeping in the back of your mind that t he inference of some of these quantities is not astraightforward thing, and that, e.g., getting the mass of a cluster can be tricky. In fact,Ask class: what are ways in which cluster mass could be inferred? Typically one gets themass from (1) motions of galaxies within the cluster, assuming they are bound, (2) thetemperature of the gas, and (3) gravitational lensing. The approximate agreement of all ofthese is encouraging.CosmologyAs we said earlier, clusters have many cosmological implications. To understand thembetter, we’ll skim the surface of a few important aspects of cosmology.The first, and most important thing, is that the universe is expanding. As you mayremember, it was this prediction of general relativity that caused Einstein to balk andintroduce the cosmological constant. The line element for the expanding universe can bewritten in many ways, one of which isds2= −dt2+dr21 + kr2/R2+ r2(dθ2+ sin2θ dφ2) . (1)Here k = 0, ±1 and the angular part indicates that this is a universe with sphericalsymmetry. In this expression R is the radius of the universe, and is time-dependent. k = 0indicates a spatially “flat” universe, which will barely expand forever, k = −1 indicates a“closed” universe that will eventually recollapse, and k = 1 indicates an “open” universe,which will expand forever. Incidentally, the time-dependence of R means that there is noglobal energy conservation in an expanding universe. One of the fundamentally usefulquantities in cosmology is the redshift, which is defined as 1 + z equaling the ratio of themeasured wavelength to the wavelength in the emitter’s rest frame.Much about the evolution and fate of the universe can be encompassed in just a fewnumbers. These are usually described in terms of their present-day contributions. It is, forexample, of interest to know if the universe will expand forever or ultimately recollapse.For this, one can define three related parameters. One is the total mass density relative toa critical density, Ωm= ρ/ρcrit. If there is nothing else in the universe but ordinary matter,Ωm< 1 means an open universe, Ωm> 1 means a closed universe, and Ωm= 1 means aflat universe. More generally, one can define a curvature parameter ΩR, such that ΩR> 0means an open universe, ΩR< 0 means a closed universe, and ΩR= 0 means a flat universe.Finally, one can define a similar contribution from the cosmological constant, ΩΛ. Ignoringcontributions from things like photons and neutrinos, Ωm+ ΩΛ+ ΩR= 1. At high redshift,regardless of what Ωm, ΩΛ, and ΩRare now, the universe acts as if Ωm= 1 and the othertwo vanish. This is important to remember, as it simplifies things dramatically at redshiftsz>∼10.Another important constant is the Hubble constant, which measures the current rate ofexpansion of the universe. This, by the way, is a misnomer, because the Hubble constantisn’t constant with redshift.The effects of the expansion of the universe are many. One of them is that whereasat low redshifts distance can be measured in many independent ways that all agree witheach other (e.g., luminosity distance, angular diameter distance, proper distance, and soon), at high redshifts they diverge from each oth er and you have to be very careful aboutwhich one you’re using at a given time. For example, when people have reported recentlythe


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