Fast power spectrum estimation

We present a new algorithm to rapidly and optimally compute power spectra. This new algorithm is based on a generalization of iterative multigrid, and has computational cost     , compared to the standard brute force approach which costs     . The procedure retains this speed on the full sky and for ill-conditioned matrices. It is applicable to galaxy power spectra, cosmic microwave background (CMB), polarization and weak lensing data. We present a mathematical convergence analysis, and performance results.     

The power of imaging spectroscopy

I demonstrate with examples from the Galactic centre the astronomical potency of imaging spectroscopy, derived by scanning a slit across a portion of sky to produce a data cube with one spectral and two spatial dimensions.     

The power of blazar jets

We estimate the power of relativistic, extragalactic jets by modelling the spectral energy distribution of a large number of blazars. We adopt a simple one-zone, homogeneous, leptonic synchrotron and inverse Compton model, taking into account seed photons originating both locally in the jet and externally. The blazars under study have an often dominant high-energy component which, if interpreted as due to inverse Compton radiation, limits the value of the magnetic field within the emission region. As a consequence, the corresponding Poynting flux cannot be energetically dominant. Also the bulk kinetic power in relativistic leptons is often smaller than the dissipated luminosity. This suggests that the typical jet should comprise an energetically dominant proton component. If there is one proton per relativistic electrons, jets radiate around 2–10 per cent of their power in high-power blazars and 3–30 per cent in less powerful BL Lacs.     

On the power in intermediate polars

I review some of the more interesting recent results on Intermediate Polars, with an emphasis on the information content of their periodic intensity variations, as provided by power spectra. The current definitions of the class are discussed, and new contenders listed with their properties. Results of the X-ray periodicities seen in IPs and developments in interpreting their light curves and power spectra are discussed. Studies of the morphology of IP X-ray light curves seem to show a bifurcation into single- or double-maxima spin profiles. An explanation for this behaviour, involving faster, weaker field, rotators accreting over a larger area, is discussed. Significant polarization has only been detected in three IPs, and the polarized flux distributions have been used to infer magnetic field strength. The failure to detect any IR cyclotron spectral features in IPs, even for polarized systems, limits our possibilities of direct magnetic field measurements. Recent tomographic results qualitatively support the accretion curtain models for IPs and some progress has been made in modelling the line emission using realistic physics.     

Expansions in power series by computer

The paper describes a technique of expanding power series solutions to sets of equations that can be applied formally to a set of equations by a compiler type program. A program suitable for an algebra system is generated that when run will produce the power series expansions by recurrence relations. Examples are given from Celestial mechanics.     

Decorrelating the power spectrum of galaxies

We show how to decorrelate the (pre-whitened) power spectrum measured from a galaxy survey into a set of high-resolution uncorrelated band-powers. The treatment includes non-linearity, 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.     

Constraining the power spectrum using clusters

We analyze an extended redshift sample of Abell/ACO clusters and compare the results with those coming from numerical simulations of the cluster distribution, based on the truncated Zel'dovich approximation (TZA), for a list of eleven dark matter (DM) models. For each model we run several realizations, so that we generate a set of 48 independent mock Abell/ACO cluster samples per model, on which we estimate cosmic variance effects. Other than the standard CDM model, we consider (a) Ω₀ = 1 CDM models based on lowering the Hubble parameter and/or on tilting the primordial spectrum; (b) Ω₀ = 1 Cold + Hot DM models with 0.1 ≤Ω_ν ≤0.5; (c) low-density flat ΛCDM models with 0.3 ≤Ω₀ ≤0.5. We compare real and simulated cluster distributions by analysing correlation statistics, the probability density function, and supercluster properties from percolation analysis. We introduce a generalized definition of the spectrum shape parameter Γ in terms of σ₂₅/σ₈, where σ_ris the rms fluctuation amplitude within a sphere of radius r. As a general result, we find that the distribution of galaxy clusters provides a constraint only on the shape of the power spectrum, but not on its amplitude: a shape parameter 0.18 Γ 0.25 and an effective spectral index at the 20 h⁻¹ Mpc scale −1.1 n_eff −0.9 are required by the Abell/ACO data. In order to obtain complementary constraints on the spectrum amplitude, we consider the cluster abundance as estimated using the Press-Schechter approach, whose reliability is explicitly tested against N-body simulations. By combining results from the analysis of the distribution and the abundance of clusters we conclude that, of the cosmological models considered here, the only viable models are either Cold + Hot DM ones with 0.2 Ω_ν 0.3, better if shared between two massive ν species, and ΛCDM ones with 0.3 Ω₀0.5.     

Optimization of the interplanetary trajectories of spacecraft with a solar electric propulsion power plant of minimal power

The problem of optimizing the interplanetary trajectories of a spacecraft (SC) with a solar electric propulsion system (SEPS) is examined. The problem of investigating the permissible power minimum of the solar electric propulsion power plant required for a successful flight is studied. Permissible ranges of thrust and exhaust velocity are analyzed for the given range of flight time and final mass of the spacecraft. The optimization is performed according to Portnyagin’s maximum principle, and the continuation method is used for reducing the boundary problem of maximal principle to the Cauchy problem and to study the solution/ parameters dependence. Such a combination results in the robust algorithm that reduces the problem of trajectory optimization to the numerical integration of differential equations by the continuation method.     

Warm dark matter versus bumpy power spectra

In this paper we explore the differences between a warm dark matter (WDM) model and a cold dark matter (CDM) model where the power on a certain scale is reduced by introducing a narrow negative feature ('dip'). This dip is placed in a way so as to mimic the loss of power in the WDM model: both models have the same integrated power out to the scale where the power of the dip model rises to the level of the unperturbed CDM spectrum again.
Using N -body simulations we show that some of the large-scale clustering patterns of this new model follow more closely the usual CDM scenario while simultaneously suppressing small-scale structures (within galactic haloes) even more efficiently than WDM. The analysis in the paper shows that the new Dip model appears to be a viable alternative to WDM, but it is based on different physics. Where WDM requires the introduction of a new particle species, the Dip model is based on a non-standard inflationary period. If we are looking for an alternative to the currently challenged standard ΛCDM structure formation scenario, neither the ΛWDM nor the new Dip model can be ruled out based on the analysis presented in this paper. They both make very similar predictions and the degeneracy between them can only be broken with observations yet to come.     

Constraining cosmological models with cluster power spectra

Using extensive N-body simulations we estimate redshift space power spectra of clusters of galaxies for different cosmological models (SCDM, TCDM, CHDM, ΛCDM, OCDM, BSI, τCDM) and compare the results with observational data for Abell–ACO clusters. Our mock samples of galaxy clusters have the same geometry and selection functions as the observational sample which contains 417 clusters of galaxies in a double cone of galactic latitude |b|>30° up to a depth of 240 h⁻¹ Mpc. The power spectrum has been estimated for wave numbers k in the range 0.03k0.2 h Mpc⁻¹. For k>k_max0.05 h Mpc⁻¹ the power spectrum of the Abell–ACO clusters has a power-law shape, P(k)∝kⁿ, with n≈−1.9, while it changes sharply to a positive slope at k<k_max. By comparison with the mock catalogues SCDM, TCDM (n=0.9), and also OCDM with Ω₀=0.35 are rejected. Better agreement with observation can be found for the ΛCDM model with Ω₀=0.35 and h=0.7 and the CHDM model with two degenerate neutrinos and Ω_HDM=0.2 as well as for a CDM model with broken scale invariance (BSI) and the τCDM model. As for the peak in the Abell–ACO cluster power spectrum, we find that it does not represent a very unusual finding within the set of mock samples extracted from our simulations.     

Orbital maneuver optimization using time-explicit power series

Orbital maneuver transfer time optimization is traditionally accomplished using direct numerical sampling to find the mission design with the lowest delta-v requirements. The availability of explicit time series solutions to the Lambert orbit determination problem allows for the total delta-v of a series of orbital maneuvers to be expressed as an algebraic function of only the individual transfer times. The delta-v function is then minimized for a series of maneuvers by finding the optimal transfer times for each orbital arc. Results are shown for the classical example of the Hohmann transfer, a noncoplanar transfer as well as an interplanetary fly-by mission to the asteroids Pallas and Juno.     

Instantaneous power radiated from magnetic dipole moments

We compute the power radiated per unit solid angle of a moving magnetic dipole moment, and its instantaneous radiated power, both non-relativistically and relativistically. This is then applied to various interesting situations: solar neutrons, electron synchrotrons and cosmological Dirac neutrinos. Concerning the latter, we show that hypothesized early-universe Big Bang conditions allow for neutrino radiation cooling and provide an energy loss-mechanism for subsequent neutrino condensation.     

Large kinetic power in FRII radio jets

We investigate the total kinetic powers (L _j) and ages (t _age) of powerful jets of four FR II radio sources (Cygnus A, 3C 223, 3C 284, and 3C 219) by the detail comparison of the dynamical model of expanding cocoons with observed ones. It is found that these sources have quite large kinetic powers with the ratio of L _j to the Eddington luminosity (L _Edd) resides in 0.02<L _j/L _Edd<10. Reflecting the large kinetic powers, we also find that the total energy stored in the cocoon (E _c) exceed the energy derived from the minimum energy condition (E _min): 2<E _c/E _min<160. This implies that a large amount of kinetic power is carried by invisible components such as thermal leptons (electron and positron) and/or protons.     

Astronomy phenomenological analysis of redshift-distance power laws

The traditional astronomical literature accepts the linear redshift-distance law on the basis of its internal consistency with accepted models of the history of the universe more than on nontrivial clearly objective tests of the linear law for directly observed quantities. The reluctance to depend on such tests rested historically on the assumed large variation in the intrinsic luminosity of extragalactic objects and a distrust of curve-fitting and statistics. But such tests are eminently feasible on the basis of modern objectively specified samples and up-to-date statistical methodology. This paper compares red-shift distance relations of the form z=k r ^p, for real values of p. Data from the visible, infrared, radio, and X-ray bands are examined. The deviation of predicted and observed apparent magnitudes, (a), and the difference between observed and predicated slope of the magnitude-log (z) plots,(b), are used to compare values of p. In summary, the p=1 values (corresponding to standard linear law) are more deviant than any other value of p, 1<p<=4for test (a) and more deviant than any value of p, 1<p<=3for test (b) except for marginal features in the smallest(radio) sample and in the lowest redshift sample. Bright subsamples and a morphologically homogeneous subsample of elliptic galaxies are also tested with similar results. In contrast, the predications for p=2 are reasonably accurate and close to optimal among all values of p explored. The p=2 case is predicted by the chronometric cosmology and in agreement with the independent analysis of Troitskii. This revised version was published online in July 2006 with corrections to the Cover Date.