6921270
Ward Identities in the derivation of Hawking radiation from Anomalies
Robinson and Wilczek suggested a new method of deriving Hawking radiation by the consideration of anomalies. The basic idea of their approach is that the flux of Hawking radiation is determined by anomaly cancellation conditions in the Schwarzschild black hole (BH) background. Iso et al. extended the method to a charged Reissner-Nordstroem BH and a rotating Kerr BH, and they showed that the flux of Hawking radiation can also be determined by anomaly cancellation conditions and regularity conditions of currents at the horizon. Their formulation gives the correct Hawking flux for all the cases at infinity and thus provides a new attractive method of understanding Hawking radiation. We present some arguments clarifying for this derivation. We show that the Ward identities and boundary conditions for covariant currents without referring to the Wess-Zumino terms and the effective action are sufficient to derive Hawking radiation. Our method, which does not use step functions, thus simplifies some of the technical aspects of the original formulation.
118416742
Tunneling Mechanism in Kerr-Newman Black Hole and Dimensional Reduction near the Horizon
It is shown that the derivation of the Hawking radiation from a rotating black hole on the basis of the tunneling mechanism is greatly simplified by using the technique of the dimensional reduction near the horizon. This technique is illustrated for the original derivation by Parikh and Wilczek, but it is readily applied to a variant of the method such as suggested by Banerjee and Majhi.
119187768
Uncertainty Relation and Probability Numerical Illustration
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty product of suitably sampled events with a very small probability. We have shown elsewhere that some examples of the evasion of the uncertainty relation noted in the past are in fact understood in this way. We here numerically illustrate that a very small uncertainty product is realized if one performs a suitable sampling of measured data that occur with a very small probability. We introduce a notion of cyclic measurements. It is also shown that our analysis is consistent with the Landau-Pollak-type uncertainty relation. It is suggested that the present analysis may help reconcile the contradicting views about the “standard quantum limit” in the detection of gravitational waves. Subject Index: 002, 060, 064
8012861
HAWKING RADIATION FROM KERR–NEWMAN BLACK HOLE AND TUNNELING MECHANISM
We present the derivation of Hawking radiation by using the tunneling mechanism in a rotating and charged black hole background. We show that the four-dimensional Kerr–Newman metric, which has a spherically nonsymmetric geometry, becomes an effectively two-dimensional spherically symmetric metric by using the technique of the dimensional reduction near the horizon. We can thus readily apply the tunneling mechanism to the nonspherical Kerr and Kerr–Newman metric.
119226694
DYNAMICAL STUDY OF A1689 FROM WIDE-FIELD VLT/VIMOS SPECTROSCOPY: MASS PROFILE, CONCENTRATION PARAMETER, AND VELOCITY ANISOTROPY
We examine the dynamics structure of the rich cluster A1689, combining VLT/VIMOS spectroscopy with Subaru/Suprime-Cam imaging. The radial velocity distribution of ~500 cluster members is bounded by a pair of clearly defined velocity caustics, with a maximum amplitude of ~|4000| km s^(–1) at ≃ 300 h^(–1) kpc, beyond which the amplitude steadily declines, approaching zero velocity at a limiting radius of ~2 h^(–1) Mpc. We derive the three-dimensional velocity anisotropy and galaxy number density profiles using a model-independent method to solve the Jeans equation, simultaneously incorporating the observed velocity dispersion profile, the galaxy counts from deep Subaru imaging, and our previously derived cluster mass profile from a joint lensing and X-ray analysis. The velocity anisotropy is found to be predominantly radial at large radius, becoming increasingly tangential towards the center, in accord with expectations. We also analyze the galaxy data independently of our previous analysis using two different methods: The first is based on a solution of the Jeans equation assuming an Navarro-Frenk-White (NFW) form for the mass distribution, whereas in the second method the caustic amplitude is used to determine the escape velocity. The cluster virial mass derived by both of these dynamical methods is in good agreement with results from our earlier lensing and X-ray analysis. We also confirm the high NFW concentration parameter, with results from both methods combined to yield c_(vir) > 13 (1σ). The inferred virial radius is consistent with the limiting radius where the caustics approach zero velocity and where the counts of cluster members drop off, suggesting that infall onto A1689 is currently not significant.
15513345
The Mass Structure of the Galaxy Cluster Cl0024+1654 from a Full Lensing Analysis of Joint Subaru and ACS/NIC3 Observations
We derive an accurate mass distribution of the rich galaxy cluster Cl0024+1654 (z = 0.395) based on deep Subaru BR{sub c} z' imaging and our recent comprehensive strong-lensing analysis of Hubble Space Telescope/Advanced Camera for Surveys/NIC3 observations. We obtain the weak-lensing distortion and magnification of undiluted samples of red and blue background galaxies by carefully combining all color and positional information. Unlike previous work, the weak and strong lensing are in excellent agreement where the data overlap. The joint mass profile continuously steepens out to the virial radius with only a minor contribution {approx}10% in the mass from known subcluster at a projected distance of {approx_equal}700 kpc h {sup -1}. The cluster light profile closely resembles the mass profile, and our model-independent M/L{sub R} profile shows an overall flat behavior with a mean of (M/L{sub R} ) {approx_equal} 230h(M/L{sub R} ){sub sun}, but exhibits a mild declining trend with increasing radius at cluster outskirts, r {approx_gt} 0.6r{sub vir}. The projected mass distribution for the entire cluster is well fitted with a single Navarro-Frenk-White model with a virial mass, M{sub vir} = (1.2 {+-} 0.2) x 10{sup 15} M{sub sun} h {sup -1}, and a concentration, c{sub vir} = 9.2{sup +1.4}{submore » -1.2}. This model fit is fully consistent with the depletion of the red background counts, providing independent confirmation. Careful examination and interpretation of X-ray and dynamical data, based on recent high-resolution cluster collision simulations, strongly suggest that this cluster system is in a post collision state, which we show is consistent with our well-defined mass profile for a major merger occurring along the line of sight, viewed approximately 2-3 Gyr after impact when the gravitational potential has had time to relax in the center, before the gas has recovered and before the outskirts are fully virialized. Finally, our full lensing analysis provides a model-independent constraint of M{sub 2D}(<r{sub vir}) = (1.4 {+-} 0.3) x 10{sup 15} M{sub sun} h {sup -1} for the projected mass of the whole system, including any currently unbound material beyond the virial radius, which can constrain the sum of the two pre-merger cluster masses when designing simulations to explore this system.« less
119279617
CLASH: NEW MULTIPLE IMAGES CONSTRAINING THE INNER MASS PROFILE OF MACS J1206.2–0847
We present a strong-lensing analysis of the galaxy cluster MACS J1206.2-0847 (z = 0.44) using UV, Optical, and IR, HST/ACS/WFC3 data taken as part of the CLASH multi-cycle treasury program, with VLT/VIMOS spectroscopy for some of the multiply lensed arcs. The CLASH observations, combined with our mass model, allow us to identify 47 new multiply lensed images of 12 distant sources. These images, along with the previously known arc, span the redshift range 1 {approx}< z {approx}< 5.5, and thus enable us to derive a detailed mass distribution and to accurately constrain, for the first time, the inner mass profile of this cluster. We find an inner profile slope of dlog {Sigma}/dlog {theta} {approx_equal} -0.55 {+-} 0.1 (in the range [1'', 53''], or 5 kpc {approx}< r {approx}< 300 kpc), as commonly found for relaxed and well-concentrated clusters. Using the many systems uncovered here we derive credible critical curves and Einstein radii for different source redshifts. For a source at z{sub s} {approx_equal} 2.5, the critical curve encloses a large area with an effective Einstein radius of {theta}{sub E} = 28'' {+-} 3'', and a projected mass of (1.34 {+-} 0.15) Multiplication-Sign 10{sup 14} M{sub Sun }. From the currentmore » understanding of structure formation in concordance cosmology, these values are relatively high for clusters at z {approx} 0.5, so that detailed studies of the inner mass distribution of clusters such as MACS J1206.2-0847 can provide stringent tests of the {Lambda}CDM paradigm.« less
119276525
Platform deformation refined pointing and phase correction for the AMiBA hexapod telescope
The Array for Microwave Background Anisotropy (AMiBA) is a radio interferometer for research in cosmology, currently operating 7 0.6m diameter antennas co-mounted on a 6m diameter platform driven by a hexapod mount. AMiBA is currently the largest hexapod telescope. We briefly summarize the hexapod operation with the current pointing error model. We then focus on the upcoming 13-element expansion with its potential difficulties and solutions. Photogrammetry measurements of the platform reveal deformations at a level which can affect the optical pointing and the receiver radio phase. In order to prepare for the 13-element upgrade, two optical telescopes are installed on the platform to correlate optical pointing tests. Being mounted on different locations, the residuals of the two sets of pointing errors show a characteristic phase and amplitude difference as a function of the platform deformation pattern. These results depend on the telescope's azimuth, elevation and polarization position. An analytical model for the deformation is derived in order to separate the local deformation induced error from the real hexapod pointing error. Similarly, we demonstrate that the deformation induced radio phase error can be reliably modeled and calibrated, which allows us to recover the ideal synthesized beam in amplitude and shape of up to 90% or more. The resulting array efficiency and its limits are discussed based on the derived errors.
14400330
Tests of AMiBA Data Integrity
We describe methods used to validate data from the Y.T. Lee Array for Microwave Background Anisotropy (AMiBA), an interferometric array designed to measure the Sunyaev-Zel'dovich effect and the anisotropy of the cosmic microwave background. We perform several statistical tests on data from pointed observations of galaxy clusters taken in 2007 and noise data from long-term blank-sky observations and measurements with the feeds covered by the absorbers. We apply power-spectrum analysis, cross-power-spectrum analysis among different outputs with different time lags in our analog correlator, and sample-variance law tests to noise data. We find that (1) there is no time variation of electronic offsets on the timescale of our two-patch observations (~10 minutes); (2) noise is correlated by less than 10% between different lags; and (3) the variance of noise scales with the inverse of time. To test the Gaussianity of the data, we apply Kolmogorov-Smirnov tests to cluster data and find that a 5% significance level efficiently detects data sets with known hardware problems without rejecting an excess of acceptable data. We also calculate third- and fourth-order moments and cumulants for the noise residual visibilities and find that about 95% of our data are within the 99% confidence regions of Gaussianity.