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A. J. S. Hamilton

Publications and source records attributed to A. J. S. Hamilton.

At least 19 recordsLinked to original sources
arXiv2013

The Black Hole Particle Accelerator as a Machine to make Baby Universes

General relativity predicts that the inner horizon of an astronomically realistic rotating black hole is subject to the mass inflation instability. The inflationary instability acts like a gravity-powered particle accelerator of extraordinary power, accelerating accreted streams of particles along the principal outgoing and ingoing null directions at the inner horizon to collision energies that would, if nothing intervened, typically exceed exponentially the Planck energy. The inflationary instability is fueled by ongoing accretion, and is occurring inevitably in essentially every black hole in our Universe. This extravagant machine, the Black Hole Particle Accelerator, has the hallmarks of a device to make baby universes. Since collisions are most numerous inside supermassive black holes, reproductive efficiency requires our Universe to make supermassive black holes efficiently, as is observed.

gr-qc↗
arXiv2011

Mass inflation in a D dimensional Reissner-Nordstrom black hole: a hierarchy of particle accelerators ?

We study the geometry inside the event horizon of perturbed D dimensional Reissner-Nordstrom-(A)dS type black holes showing that, similarly to the four dimensional case, mass inflation also occurs for D>4. First, using the homogeneous approximation, we show that an increase of the number of spatial dimensions contributes to a steeper variation of the metric coefficients with the areal radius and that the phenomenon is insensitive to the cosmological constant in leading order. Then, using the code reported in arXiv:0904.2669 [gr-qc] adapted to D dimensions, we perform fully non-linear numerical simulations. We perturb the black hole with a compact pulse adapting the pulse amplitude such that the relative variation of the black hole mass is the same in all dimensions, and determine how the black hole interior evolves under the perturbation. We qualitatively confirm that the phenomenon is similar to four dimensions as well as the behaviour observed in the homogeneous approximation. We speculate about the formation of black holes inside black holes triggered by mass inflation, and about possible consequences of this scenario.

gr-qc↗
arXiv2009

Mass Inflation in Brans-Dicke gravity

A detailed non-linear analysis of the internal structure of spherical, charged black holes that are accreting scalar matter is performed in the framework of the Brans-Dicke theory of gravity. We choose the lowest value of the Brans-Dicke parameter that is compatible with observational constraints. First, the homogeneous approximation is used. It indicates that mass inflation occurs and that the variations of the Brans-Dicke scalar inside the black hole, which could in principle be large in the absence of mass inflation, become small when mass inflation does occur. Then, a full non-linear numerical study of the black hole interior perturbed by a self-gravitating massless uncharged scalar-field is performed. We use an algorithm with adaptive mesh refinement capabilities. In this way, the changes in the internal structure of the black hole caused by mass inflation are determined, as well as the induced variations of the Brans-Dicke scalar, confirming, qualitatively, the indications given by the homogeneous approximation.

gr-qc↗
arXiv2007

Perturbation theory of spherically symmetric self-similar black holes

The theory of perturbations of spherically symmetric self-similar black holes is presented, in the Newman-Penrose formalism. It is shown that the wave equations for gravitational, electromagnetic, and scalar waves are separable, though not decoupled. A generalization of the Teukolsky equation is given. Monopole and dipole modes are treated. The Newman-Penrose wave equations governing polar and axial spin-0 perturbations are explored.

gr-qc↗
arXiv2006

On measuring the covariance matrix of the nonlinear power spectrum from simulations

We show how to estimate the covariance of the power spectrum of a statistically homogeneous and isotropic density field from a single periodic simulation, by applying a set of weightings to the density field, and by measuring the scatter in power spectra between different weightings. We recommend a specific set of 52 weightings containing only combinations of fundamental modes, constructed to yield a minimum variance estimate of the covariance of power. Numerical tests reveal that at nonlinear scales the variance of power estimated by the weightings method substantially exceeds that estimated from a simple ensemble method. We argue that the discrepancy is caused by beat-coupling, in which products of closely spaced Fourier modes couple by nonlinear gravitational growth to the beat mode between them. Beat-coupling appears whenever nonlinear power is measured from Fourier modes with a finite spread of wavevector, and is therefore present in the weightings method but not the ensemble method. Beat-coupling inevitably affects real galaxy surveys, whose Fourier modes have finite width. Surprisingly, the beat-coupling contribution dominates the covariance of power at nonlinear scales, so that, counter-intuitively, it is expected that the covariance of nonlinear power in galaxy surveys is dominated not by small scale structure, but rather by beat-coupling to the largest scales of the survey.

astro-ph↗
arXiv2006

Information content of the non-linear power spectrum: the effect of beat-coupling to large scales

We measure the covariance of the non-linear matter power spectrum from N-body simulations using two methods. In the first case, the covariance of power is estimated from the scatter over many random realizations of the density field. In the second, we use a novel technique to measure the covariance matrix from each simulation individually by re-weighting the density field with a carefully chosen set of functions. The two methods agree at linear scales, but unexpectedly they disagree substantially at increasingly non-linear scales. Moreover, the covariance of non-linear power measured using the re-weightings method changes with box size. The numerical results are consistent with an explanation given in a companion paper, which argues that the cause of the discrepancy is beat-coupling, in which products of Fourier modes separated by a small wavevector couple by gravitational growth to the large-scale beat mode between them. We calculate the information content of the non-linear power spectrum (about the amplitude of the initial, linear power spectrum) using both methods and confirm the result of a previous paper, that at translinear scales the power spectrum contains little information over and above that in the linear power spectrum, but that there is a marked increase in information at non-linear scales. We suggest that, in real galaxy surveys, the covariance of power at non-linear scales is likely to be dominated by beat-coupling to the largest scales of the survey and that, as a result, only part of the information potentially available at non-linear scales is actually measurable from real galaxy surveys.

astro-ph↗
arXiv2005

Information content of the non-linear matter power spectrum

We use an ensemble of N-body simulations of the currently favoured (concordance) cosmological model to measure the amount of information contained in the non-linear matter power spectrum about the amplitude of the initial power spectrum. Two surprising results emerge from this study: (i) that there is very little independent information in the power spectrum in the translinear regime (k ~ 0.2-0.8 Mpc/h at the present day) over and above the information at linear scales and (ii) that the cumulative information begins to rise sharply again with increasing wavenumber in the non-linear regime. In the fully non-linear regime, the simulations are consistent with no loss of information during translinear and non-linear evolution. If this is indeed the case then the results suggest a picture in which translinear collapse is very rapid, and is followed by a bounce prior to virialization, impelling a wholesale revision of the HKLM-PD formalism.

astro-ph↗
arXiv2003

A scheme to deal accurately and efficiently with complex angular masks in galaxy surveys

This paper presents a scheme to deal accurately and efficiently with complex angular masks, such as occur typically in galaxy surveys. An angular mask is taken to be an arbitrary union of arbitrarily weighted angular regions bounded by arbitrary numbers of edges. The restrictions on the mask are (i) that each edge must be part of some circle on the sphere (but not necessarily a great circle), and (ii) that the weight within each subregion of the mask must be constant. The scheme works by resolving a mask into disjoint polygons, convex angular regions bounded by arbitrary numbers of edges. The polygons may be regarded as the `pixels' of a mask, with the feature that the pixels are allowed to take a rather general shape, rather than following some predefined regular pattern. Among other things, the scheme includes facilities to compute the spherical harmonics of the angular mask, and Data-Random and Random-Random angular integrals. A software package mangle which implements this scheme, along with complete software documentation, is available at http://casa.colorado.edu/~ajsh/mangle/ .

astro-ph↗
arXiv2001

Constraints on inflation from CMB and Lyman-alpha forest

We constrain the spectrum of primordial curvature perturbations by using recent Cosmic Microwave Background (CMB) and Large Scale Structure (LSS) data. Specifically, we consider CMB data from the COBE, Boomerang and Maxima experiments, the real space galaxy power spectrum from the IRAS PSCz survey, and the linear matter power spectrum inferred from Ly-alpha forest spectra. We study the case of single field slow roll inflationary models, and we extract bounds on the scalar spectral index, n, the tensor to scalar ratio, r, and the running of the scalar spectral index, dlnk, for various combinations of the observational data. We find that CMB data, when combined with data from Lyman-alpha forest, place strong constraints on the inflationary parameters. Specifically, we obtain n \approx 0.9, r < 0.3 and dlnk \approx 0, indicating that single field hybrid models are ruled out.

astro-ph↗
arXiv2000

Linear Redshift Distortions and Power in the PSCz Survey

We present a state-of-the-art linear redshift distortion analysis of the recently published IRAS Point Source Catalog Redshift Survey (PSCz). The procedure involves linear compression into 4096 Karhunen-Loeve modes culled from a potential pool of about 3 x 10^5 modes, followed by quadratic compression into three separate power spectra, the galaxy-galaxy, galaxy-velocity, and velocity-velocity power spectra. Least squares fitting to the decorrelated power spectra yields a linear redshift distortion parameter beta = Omega_m^0.6/b = 0.41(+0.13,-0.12).

astro-ph↗
arXiv2000

Uncorrelated Modes of the Nonlinear Power Spectrum

Nonlinear evolution causes the galaxy power spectrum to become broadly correlated over different wavenumbers. It is shown that prewhitening the power spectrum - transforming the power spectrum in such a way that the noise covariance becomes proportional to the unit matrix - greatly narrows the covariance of power. The eigenfunctions of the covariance of the prewhitened nonlinear power spectrum provide a set of almost uncorrelated nonlinear modes somewhat analogous to the Fourier modes of the power spectrum itself in the linear, Gaussian regime. These almost uncorrelated modes make it possible to construct a near minimum variance estimator and Fisher matrix of the prewhitened nonlinear power spectrum analogous to the Feldman-Kaiser-Peacock estimator of the linear power spectrum. The paper concludes with summary recipes, in gourmet, fine, and fastfood versions, of how to measure the prewhitened nonlinear power spectrum from a galaxy survey in the FKP approximation. An Appendix presents FFTLog, a code for taking the fast Fourier or Hankel transform of a periodic sequence of logarithmically spaced points, which proves useful in some of the manipulations.

astro-ph↗
arXiv2000

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.

astro-ph↗
arXiv1997

Redshift Distortions and Omega in IRAS Surveys

Redshift space distortions on large scales can be used to measure the linear growth rate parameter $\ff \approx Ω^{0.6}/b$. I report here measurements of such distortions in the IRAS 2 Jy, 1.2 Jy, and QDOT redshift surveys, finding $\ff = 0.69^{+ .21}_{- .19}$ from a merged QDOT plus 1.2 Jy catalogue. Unfortunately, confidence in this result is undermined by a marked ($4σ$) change in the pattern of clustering in QDOT beyond about $80 h^{-1} Mpc$. A similar effect may be present at a mild level in the 1.2 Jy survey. The effect may be caused by systematic variation in the effective flux limit of the IRAS PSC over the sky, with a dispersion of $\sim 0.1$ Jy on scales $\sim 7^{\circ}$. If so, then the value of $\ff$ inferred from redshift distortions in IRAS surveys may be systematically underestimated.

astro-ph↗
arXiv1997

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 $β\approx Ω^{0.6}/b$, where $Ω$ 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 $β$ 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.

astro-ph↗
arXiv1997

Linear Redshift Distortions: A Review

Redshift maps of galaxies in the Universe are distorted by the peculiar velocities of galaxies along the line of sight. The amplitude of the distortions on large, linear scales yields a measurement of the linear redshift distortion parameter, which is $β\approx Ω_0^{0.6}/b$ in standard cosmology with cosmological density $Ω_0$ and light-to-mass bias $b$. All measurements of $β$ from linear redshift distortions published up to mid 1997 are reviewed. The average and standard deviation of the reported values is $β_{optical} = 0.52 \pm 0.26$ for optically selected galaxies, and $β_{IRAS} = 0.77 \pm 0.22$ for IRAS selected galaxies. The implied relative bias is $b_{optical}/b_{IRAS} \approx 1.5$. If optical galaxies are unbiased, then $Ω_0 = 0.33^{+0.32}_{-0.22}$, while if IRAS galaxies are unbiased, then $Ω_0 = 0.63^{+0.35}_{-0.27}$.

astro-ph↗
arXiv1997

Towards Optimal Measurement of Power Spectra I: Minimum Variance Pair Weighting and the Fisher Matrix

This is the first of a pair of papers which address the problem of measuring the unredshifted power spectrum in optimal fashion from a survey of galaxies, with arbitrary geometry, for Gaussian or non-Gaussian fluctuations, in real or redshift space. In this first paper, that pair weighting is derived which formally minimizes the expected variance of the unredshifted power spectrum windowed over some arbitrary kernel. The inverse of the covariance matrix of minimum variance estimators of windowed power spectra is the Fisher information matrix, which plays a central role in establishing optimal estimators. Actually computing the minimum variance pair window and the Fisher matrix in a real survey still presents a formidable numerical problem, so here a perturbation series solution is developed. The properties of the Fisher matrix evaluated according to the approximate method suggested here are investigated in more detail in the second paper.

astro-ph↗
arXiv1997

Towards Optimal Measurement of Power Spectra II: A Basis of Positive, Compact, Statistically Orthogonal Kernels

This is the second of two papers which address the problem of measuring the unredshifted power spectrum of fluctuations from a galaxy survey in optimal fashion. A key quantity is the Fisher matrix, which is the inverse of the covariance matrix of minimum variance estimators of the power spectrum of the survey. It is shown that bases of kernels which give rise to complete sets of statistically orthogonal windowed power spectra are obtained in general from the eigenfunctions of the Fisher matrix scaled by some arbitrary positive definite scaling matrix. Among the many possible bases of kernels, there is a basis, obtained by applying an infinitely steep scaling function, which leads to kernels which are positive and compact in Fourier space. This basis of kernels, along with the associated minimum variance pair weighting derived in the previous paper, would appear to offer a solution to the problem of how to measure the unredshifted power spectrum optimally. Illustrative kernels are presented for the case of the PSCz survey.

astro-ph↗