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

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Weak Lensing Dilution in A1689 Note that the peak value is rather large, equivalent to M/L B ∼ 400h(M/L) ⊙ in the restframe B-band often used as a reference, but the mass of A1689 is at the extreme end of the cluster population, M ∼ 2 × 10 15 hM ⊙ (Broadhurst et al. 2005b), and given the general tendency of M/L to increase with increasing mass, from galaxies through groups to clusters, we may not be surprised to find the peak to somewhat exceed the typical range for clusters, 150 − 300hM/L B ⊙ (Carlberg et al. 2001). The general profile of M/L is similar in form to that derived for CL 0152-1357 by Jee et al. (2005) based on a careful weak lensing analysis of recent deep ACS images. We have also constructed a profile of the total mass to stellar mass M/M ∗ ratio (red curves in Fig. 2.18 and Fig.2.19). This is arguably a more physically useful indicator of the relationship between dark and luminous matter compared to the ratio of M/L, because the starlight can be strongly influenced by the presence of relatively small numbers of luminous hot stars. To calculate M/M ∗ we make use of the color profile derived in § 2.7, and an empirical relationship between color and the ratio M ∗ /L for stellar populations established for local galaxies in the the SDSS survey by Bell et al. (2003). The slope of the projected stellar mass profile, d log(M ∗ )/d log(r) = −1.15 ± 0.13, derived this way is slightly steeper than the luminosity profile, as expected. The observed relation we derive this way is somewhat flatter than for M/L and the mean contribution by mass for stars is about 1.25% for this cluster and similar to a mean value of ∼ 2% derived from a carefully selected sample of local clusters by Biviano & Salucci (2006). 2.10 Cluster mass profile We use the combined distortion information obtained from the ACS and Subaru imaging, as described above (Fig. 2.6) and compare with models for the mass distribution. We have improved on our earlier distortion measurements made with Subaru, with the addition of the background blue galaxy population defined here, so that the significance of the distortion measurements is somewhat greater than our earlier work which was based only on the red 60
2.10 Cluster mass profile sample (Broadhurst et al. 2005b). In addition, we have extended the distortion measurements to the central region using the HST /ACS information, as described in § 2.4, where we have clearly identified a maximum and a minimum value of g T , which accurately correspond to the tangential and radial critical curves (Fig. 2.20), independently derived from the the many giant tangential and radial arcs observed for this cluster (see Broadhurst et al. 2005a). Here we test the universal parameterization of CDM-based mass profiles advocated by Navarro et al. (1997). This model profile is weighted over the differing results from sets of halos identified in N-body simulations. A cluster profile is summed over all the mass contained within the main halo, including the galactic halos. Hence, we compare the integrated mass profile we deduced directly with the NFW predictions without having to invent a prescription to remove the cluster galaxies. NFW have shown that massive CDM hales are predicted to be less concentrated with increasing halo mass, a trend identified with collapse redshift, which is generally higher for smaller halos following from the steep evolution of the cosmological density of matter. The most massive bound structures form later in hierarchical models and therefore clusters are anticipated to have a relatively low concentration, quantified by the ratio C vir = r virial /r s . In the context of this model, the predicted form of CDM dominated are predicted to follow a density profile lacking a core, but with a much shallower central profile (r ≤ 100 h −1 kpc) than a purely isothermal body. The fit to an NFW profile is made keeping r s , and ρ s , the characteristic radius and the corresponding density, as free parameters. These can be adjusted to normalize the model to the observed maximum in the distortion profile at the tangential critical radius of ≃ 45 ′′ . The combination of these parameters then fixes the degree of concentration, and the corresponding lensing distortion profile can then be calculated. Integrating the mass along a column, z, where r 2 = (ξ r r s ) 2 +z 2 gives: ∫ ξ ∫ ∞ M(ξ) = ρ s rs(ξ) 3 d 2 1 dz ξ . (2.24) o −∞ (r/r s )(1 + r/r s ) 2 r s 61
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TELAVIVUNIVERSITY SCHOOLOFPHYSICS&A
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To my parents
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1.2.3 Weak Gravitational Lensing .
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5 Discussion 139 5.1 Summary . . .
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negligibly contaminated by the clus
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Chapter 1 Introduction Clusters of
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1.1 Clusters of Galaxies The space
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Chapter 4 A Weak Lensing Determinat
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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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כפי שמתואר בפרק השל
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עבודה זו נעשתה בהנח
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