Mass and Light distributions in Clusters of Galaxies - Henry A ...

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Introduction assembly. 1.1.4 Luminosity Function of Galaxies in Clusters The luminosity function (LF) of galaxies in a cluster gives the distribution of luminosities of galaxies. LFs are often defined in terms of magnitudes, m ∝ −2.5 log 10 (L). There are several LF forms commonly used. Schechter (1976) introduced an analytic approximation for the differential LF φ(L)dL = N ∗ (L/L ∗ ) −α e −L/L∗ d(L/L ∗ ) (1.14) where L ∗ is a characteristic luminosity, and α is the faint-end slope. The parameter N ∗ is a useful measure of the richness of the cluster. The parameter L ∗ usually denotes the break in the LF, hence it represents a characteristic luminosity of cluster galaxies. It is found that L ∗ is similar for many clusters, corresponding to an absolute magnitude of MV ∗ ≈ −21.9 + 5 log 10 h 50 . The advantages of the Schechter function are that it is analytical and continuous. An expression for the mass function similar to the Schechter form was predicted by a simple analytical model for galaxy formation (Press & Schechter 1974). While the Schechter function serves as a good fit to the majority of clusters, there are a number of clusters that show a departure from it. These departures include variations in the values of M ∗ and α, corresponding to the cluster morphology (Oemler 1974; Dressler 1978). They probably stem from the conditions of the cluster at its formation epoch. Variations in the steepness of the bright end may reflect evolutionary changes, such as tidal interactions or merging of massive galaxies (Richstone 1975; Hausman & Ostriker 1978). For example, steep bright-end often fits to clusters that have bright cD galaxies, indicating many massive galaxies were merged to form the cD (Dressler 1978). 8
1.1 Clusters of Galaxies 1.1.5 X-ray Observations of Clusters X-ray observations probe the gas component of the cluster. It has been established that the majority of the baryonic matter is in the form of hot intracluster (IC) gas, with only about 3% residing within stars in galaxies. Probing IC gas can reveal unique insight into the physical processes that govern galaxy formation, and the gas properties can be used to determine the total cluster mass, in clusters that are in hydrostatic equilibrium. Spectral X-ray observations yield the gas temperature, in the range of 3−15 keV, while its density is determined from the spatial profile of the (thermal Bremsstrahlung) emission. Spectroscopic measurements of the emission lines (mostly of the strong K α line complex of Fe 24+ ) reveal that IC gas is metal enriched with typically 1/3 solar abundances. X-ray imaging has progressed significantly in the past decade by detailed measurements with the Chandra and XMM-Newton telescopes that yield high-resolution spatial mapping of the distribution of intracluster gas. From measurement of the temperature and density profiles the gas pressure and entropy distributions can be derived. When combining density and temperature profiles the total mass of the cluster can be deduced from a solution of the hydrostatic equilibrium equation. Detailed X-ray images can also yield information on whether the cluster is relaxed or has substructure due to ongoing dynamical processes, such as merging of galaxies or groups. Many clusters seem to be in hydrostatic equilibrium. Assuming spherical symmetry, the total gravitating mass within the virial radius R is then, M(< R) = − k ( BT R d ln ρg Gµm p d ln R + d ln T ) , (1.15) d ln R where ρ g is the gas density, and µm p is the mean mass per plasma particle. Thus, the total cluster mass can be inferred from X-ray measurements of the gas density and temperature profiles. IC gas is commonly modeled with a 9
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Chapter 3 Detailed Cluster Mass and
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3.6 Weak lensing analysis 3.6 Weak
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3.8 Cluster light profiles 600 A168
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3.9 M/L profiles Broadhurst et al.
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3.9 M/L profiles very moderate decl
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4.1 Introduction Zitrin et al. 2009
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References Abadi, M. G., Moore, B.,
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REFERENCES Broadhurst, T., Umetsu,
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REFERENCES Gaidos, E. J. 1997, AJ,
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REFERENCES Kaiser, N. 1995, ApJ, 43
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REFERENCES Natarajan, P., Loeb, A.,
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REFERENCES Schrabback, T. et al. 20
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כפי שמתואר בפרק השל
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עבודה זו נעשתה בהנח
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