Spherical Redshift Distortions

Peculiar velocities induce apparent line of sight displacements of galaxies in redshift space, distorting the pattern of clustering in the radial versus transverse directions. On large scales, the amplitude of the distortion yields a measure of the dimensionless linear growth rate $\beta \approx \Omega^{0.6}/b$, where $\Omega$ is the cosmological density and $b$ the linear bias factor. To make the maximum statistical use of the data in a wide angle redshift survey, and for the greatest accuracy, the spherical character of the distortion needs to be treated properly, rather than in the simpler plane parallel approximation. In the linear regime, the redshift space correlation function is described by a spherical distortion operator acting on the true correlation function. It is pointed out here that there exists an operator, which is essentially the logarithmic derivative with respect to pair separation, which both commutes with the spherical distortion operator, and at the same time defines a characteristic scale of separation. The correlation function can be expanded in eigenfunctions of this operator, and these eigenfunctions are eigenfunctions of the distortion operator. Ratios of the observed amplitudes of the eigenfunctions yield measures of the linear growth rate $\beta$ in a manner independent of the shape of the correlation function. More generally, the logarithmic derivative $\partial/\partial\ln r$ with respect to depth $r$, along with the square $L^2$ and component $L_z$ of the angular momentum operator, form a complete set of commuting operators for the spherical distortion operator acting on the density. The eigenfunctions of this complete set of operators are spherical waves about the observer, with radial part lying in logarithmic real or Fourier space.Comment: 15 pages, with 1 embedded EPS figur

A note on dual giant gravitons in AdS4×CP3AdS_{4}\times \mathbb{CP}^{3}

We study some of the properties of dual giant gravitons - D2-branes wrapped on an $S^{2}\subset AdS_{4}$ - in type IIA string theory on $AdS_{4}\times \mathbb{CP}^{3}$. In particular we confirm that the spectrum of small fluctuations about the giant is both real and independent of the size of the graviton. We also extend previously developed techniques for attaching open strings to giants to this D2-brane giant and focus on two particular limits of the resulting string sigma model: In the pp-wave limit we quantize the string and compute the spectrum of bosonic excitations while in the semiclassical limit, we read off the fast string Polyakov action and comment on the comparison to the Landau-Lifshitz action for the dual open spin chain.Comment: v3 significantly changed: added coupling to RR 1-form and turned on worldvolume gauge field, computed gauge field fluctuation, added comments on closure of the sl(2) sector and re-written to improve clarity. This version published in JHE

Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit

Volumes of sub-wavelength electromagnetic elements can act like homogeneous materials: metamaterials. In analogy, sheets of optical elements such as prisms can act ray-optically like homogeneous sheet materials. In this sense, such sheets can be considered to be metamaterials for light rays (METATOYs). METATOYs realize new and unusual transformations of the directions of transmitted light rays. We study here, in the ray-optics and scalar-wave limits, the wave-optical analog of such transformations, and we show that such an analog does not always exist. Perhaps, this is the reason why many of the ray-optical possibilities offered by METATOYs have never before been considered.Comment: 10 pages, 3 figures, references update

Local light-ray rotation

We present a sheet structure that rotates the local ray direction through an arbitrary angle around the sheet normal. The sheet structure consists of two parallel Dove-prism sheets, each of which flips one component of the local direction of transmitted light rays. Together, the two sheets rotate transmitted light rays around the sheet normal. We show that the direction under which a point light source is seen is given by a Mobius transform. We illustrate some of the properties with movies calculated by ray-tracing software.Comment: 9 pages, 6 figure

Measuring the galaxy power spectrum with future redshift surveys

Precision measurements of the galaxy power spectrum P(k) require a data analysis pipeline that is both fast enough to be computationally feasible and accurate enough to take full advantage of high-quality data. We present a rigorous discussion of different methods of power spectrum estimation, with emphasis on the traditional Fourier method, the linear (Karhunen-Loeve; KL), and quadratic data compression schemes, showing in what approximations they give the same result. To improve speed, we show how many of the advantages of KL data compression and power spectrum estimation may be achieved with a computationally faster quadratic method. To improve accuracy, we derive analytic expressions for handling the integral constraint, since it is crucial that finite volume effects are accurately corrected for on scales comparable to the depth of the survey. We also show that for the KL and quadratic techniques, multiple constraints can be included via simple matrix operations, thereby rendering the results less sensitive to galactic extinction and mis-estimates of the radial selection function. We present a data analysis pipeline that we argue does justice to the increases in both quality and quantity of data that upcoming redshift surveys will provide. It uses three analysis techniques in conjunction: a traditional Fourier approach on small scales, a pixelized quadratic matrix method on large scales and a pixelized KL eigenmode analysis to probe anisotropic effects such as redshift-space distortions.Comment: Major revisions for clarity. Matches accepted ApJ version. 23 pages, with 2 figs included. Color figure and links at http://www.sns.ias.edu/~max/galpower.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/galpower.html (faster from Europe) or from [email protected]

Decorrelating the Power Spectrum of Galaxies

It is shown how to decorrelate the (prewhitened) power spectrum measured from a galaxy survey into a set of high resolution uncorrelated band-powers. The treatment includes nonlinearity, but not redshift distortions. Amongst the infinitely many possible decorrelation matrices, the square root of the Fisher matrix, or a scaled version thereof, offers a particularly good choice, in the sense that the band-power windows are narrow, approximately symmetric, and well-behaved in the presence of noise. We use this method to compute band-power windows for, and the information content of, the Sloan Digital Sky Survey, the Las Campanas Redshift Survey, and the IRAS 1.2 Jy Survey.Comment: 11 pages, including 8 embedded PostScript figures. Minor changes to agree with published versio

The power spectrum of galaxies in the 2dF 100k redshift survey

We compute the real-space power spectrum and the redshift-space distortions of galaxies in the 2dF 100k galaxy redshift survey using pseudo-Karhunen-Loeve eigenmodes and the stochastic bias formalism. Our results agree well with those published by the 2dFGRS team, and have the added advantage of producing easy-to-interpret uncorrelated minimum-variance measurements of the galaxy-galaxy, galaxy-velocity and velocity-velocity power spectra in 27 k-bands, with narrow and well-behaved window functions in the range 0.01h/Mpc < k < 0.8h/Mpc. We find no significant detection of baryonic wiggles, although our results are consistent with a standard flat Omega_Lambda=0.7 ``concordance'' model and previous tantalizing hints of baryonic oscillations. We measure the galaxy-matter correlation coefficient r > 0.4 and the redshift-distortion parameter beta=0.49+/-0.16 for r=1 (beta=0.47+/- 0.16 without finger-of-god compression). Since this is an apparent-magnitude limited sample, luminosity-dependent bias may cause a slight red-tilt in the power spectum. A battery of systematic error tests indicate that the survey is not only impressive in size, but also unusually clean, free of systematic errors at the level to which our tests are sensitive. Our measurements and window functions are available at http://www.hep.upenn.edu/~max/2df.html together with the survey mask, radial selection function and uniform subsample of the survey that we have constructed.Comment: Replaced to match accepted MNRAS version, with new radial/angular systematics plot and sigma8 typo corrected. High-res figures, power spectra, windows and our uniform galaxy subsample with mask at http://www.hep.upenn.edu/~max/2df.html or from [email protected]. 26 journal pages, 28 fig

HST Images and Spectra of the Remnant of SN 1885 in M31

Near UV HST images of the remnant of SN 1885 (S And) in M31 show a 0"70 +- 0"05 diameter absorption disk silhouetted against M31's central bulge, at SN 1885's historically reported position. The disk's size corresponds to a linear diameter of 2.5 +- 0.4 pc at a distance of 725 +- 70 kpc, implying an average expansion velocity of 11000 +- 2000 km/s over 110 years. Low-dispersion FOS spectra over 3200-4800 A; reveal that the absorption arises principally from Ca II H & K (equivalent width ~215 A;) with weaker absorption features of Ca I 4227 A; and Fe I 3720 A;. The flux at Ca II line center indicates a foreground starlight fraction of 0.21, which places SNR 1885 some 64 pc to the near side of the midpoint of the M31 bulge, comparable to its projected 55 pc distance from the nucleus. The absorption line profiles suggest an approximately spherically symmetric, bell-shaped density distribution of supernova ejecta freely expanding at up to 13100 +- 1500 km/s. We estimate Ca I, Ca II, and Fe I masses of 2.9(+2.4,-0.6) x 10^-4 M_o, 0.005(+0.016,-0.002) M_o, and 0.013(+0.010,-0.005) M_o respectively. If the ionization state of iron is similar to the observed ionization state of calcium, M_CaII/M_CaI = 16(+42,-5), then the mass of Fe II is 0.21(+0.74,-0.08) M_o, consistent with that expected for either normal or subluminous SN Ia.Comment: 8 pages, including 4 embedded EPS figures, emulateapj.sty style file. Color image at http://casa.colorado.edu/~mcl/sand.shtml . Submitted to Ap

Determination of the Baryon Density from Large Scale Galaxy Redshift Surveys

We estimate the degree to which the baryon density, $\Omega_{b}$, can be determined from the galaxy power spectrum measured from large scale galaxy redshift surveys, and in particular, the Sloan Digital Sky Survey. A high baryon density will cause wiggles to appear in the power spectrum, which should be observable at the current epoch. We assume linear theory on scales $\geq 20h^{-1}Mpc$ and do not include the effects of redshift distortions, evolution, or biasing. With an optimum estimate of $P(k)$ to $k\sim 2\pi/(20 h^{-1} Mpc)$, the $1 \sigma$ uncertainties in $\Omega_{b}$ are roughly 0.07 and 0.016 in flat and open ($\Omega_{0}=0.3$) cosmological models, respectively. This result suggests that it should be possible to test for consistency with big bang nucleosynthesis estimates of $\Omega_{b}$ if we live in an open universe.Comment: 23 Pages, 10 Postscript figure