Evidence for the deficiency of short cosmic ray pathlengths and a physically realistic explanation — The no-near-sources model

From our recent observations of the charge and energy spectra of cosmic-ray nuclei we have constructed secondary-to-primary charge ratios at the two ends of the charge spectrum. These ratios are found to be inconsistent with thead hoc leaky-box model of cosmic-ray propagation which leads to an exponential pathlength distribution. Models for which the pathlength distribution function is deficient in short pathlengths provide a more consistent picture. Several of these models are investigated, bothad hoc and physical. The physical model considered here is one for which detailed galactic propagation parameters and boundary conditions are used and for which there exists no near sources of cosmic rays over a time interval corresponding to a few times the cosmic-ray age.     

GZK cutoff distortion due to the energy error distribution shape

The development of an ultra high energy air shower has an intrinsic energy fluctuation due both to the first interaction point and to the cascade development. Here we show that for a given primary energy this fluctuation has a lognormal distribution and thus observations will estimate the primary energy with a lognormal error distribution. We analyze the UHECR energy spectrum convolved with the lognormal energy error and demonstrate that the shape of the error distribution will interfere significantly with the ability to observe features in the spectrum. If the standard deviation of the lognormal error distribution is equal or larger than 0.25, both the shape and the normalization of the measured energy spectra will be modified significantly. As a consequence, the GZK cutoff might be sufficiently smeared as not to be seen (without very high statistics). This result is independent of the power law of the cosmological flux. As a conclusion we show that in order to establish the presence or not of the GZK feature, not only more data are needed but also that the shape of the energy error distribution has to be known well. The high energy tail and the sigma of the approximate lognormal distribution of the error in estimating the energy must be at the minimum set by the physics of showers.     

GZK cutoff distortion due to the energy error distribution shape

The development of an ultra high energy air shower has an intrinsic energy fluctuation due both to the first interaction point and to the cascade development. Here we show that for a given primary energy this fluctuation has a lognormal distribution and thus observations will estimate the primary energy with a lognormal error distribution. We analyze the UHECR energy spectrum convolved with the lognormal energy error and demonstrate that the shape of the error distribution will interfere significantly with the ability to observe features in the spectrum. If the standard deviation of the lognormal error distribution is equal or larger than 0.25, both the shape and the normalization of the measured energy spectra will be modified significantly. As a consequence, the GZK cutoff might be sufficiently smeared as not to be seen (without very high statistics). This result is independent of the power law of the cosmological flux. As a conclusion we show that in order to establish the presence or not of the GZK feature, not only more data are needed but also that the shape of the energy error distribution has to be known well. The high energy tail and the sigma of the approximate lognormal distribution of the error in estimating the energy must be at the minimum set by the physics of showers.     

Probing magnetic turbulence by synchrotron polarimetry: statistics and structure of magnetic fields from Stokes correlators

We describe a novel technique for probing the statistical properties of cosmic magnetic fields based on radio polarimetry data. Second-order magnetic field statistics like the power spectrum cannot always distinguish between magnetic fields with essentially different spatial structure. Synchrotron polarimetry naturally allows certain fourth-order magnetic field statistics to be inferred from observational data, which lifts this degeneracy and can thereby help us gain a better picture of the structure of the cosmic fields and test theoretical scenarios describing magnetic turbulence. In this work we show that a fourth-order correlator of specific physical interest, the tension force spectrum, can be recovered from the polarized synchrotron emission data. We develop an estimator for this quantity based on polarized emission observations in the Faraday rotation free frequency regime. We consider two cases: a statistically isotropic field distribution, and a statistically isotropic field superimposed on a weak mean field. In both cases the tension force power spectrum is measurable; in the latter case, the magnetic power spectrum may also be obtainable. The method is exact in the idealized case of a homogeneous relativistic electron distribution that has a power-law energy spectrum with a spectral index of   p = 3  , and assumes statistical isotropy of the turbulent field. We carry out numerical tests of our method using synthetic polarized emission data generated from numerically simulated magnetic fields. We show that the method is valid, that it is not prohibitively sensitive to the value of the electron spectral index p , and that the observed tension force spectrum allows one to distinguish between e.g. a randomly tangled magnetic field (a default assumption in many studies) and a field organized in folded flux sheets or filaments.     

Non-linear evolution of suppressed dark matter primordial power spectra

We address the degree and rapidity of generation of small-scale power over the course of structure formation in cosmologies where the primordial power spectrum is strongly suppressed beyond a given wavenumber. We first summarize the situations where one expects such suppressed power spectra and point out their diversity. We then employ an exponential cut-off, which characterizes warm dark matter (WDM) models, as a template for the shape of the cut-off and focus on damping scales ranging from 10⁶ to  10⁹  h ⁻¹ M_⊙  . Using high-resolution simulations, we show that the suppressed part of the power spectrum is quickly (re)generated and catches up with both the linear and the non-linear evolution of the unsuppressed power spectrum. From   z = 2  onwards, a power spectrum with a primordial cut-off at  10⁹  h ⁻¹ M_⊙  becomes virtually indistinguishable from an evolved cold dark matter (CDM) power spectrum. An attractor such as that described in Zaldarriaga, Scoccimarro & Hui for power spectra with different spectral indices also emerges in the case of truncated power spectra. Measurements of   z ∼ 0  non-linear power spectra at  ∼100  h ⁻¹ kpc  cannot rule out the possibility of linear power spectra damped below  ∼10⁹  h ⁻¹ M_⊙  . Therefore, WDM or scenarios with similar features should be difficult to exclude in this way.     

Broadening of QSO Lyα forest absorbers

We investigate the dependence of QSO Ly α absorption features on the temperature of the absorbing gas and on the amplitude of the underlying dark-matter fluctuations. We use high-resolution hydrodynamic simulations in cold dark matter dominated cosmological models. In models with a hotter intergalactic medium (IGM), the increased temperature enhances the pressure gradients between low- and high-density regions and this changes the spatial distribution and the velocity field of the gas. Combined with more thermal broadening, this leads to significantly wider absorption features in hotter models. Cosmological models with little small-scale power also have broader absorption features, because fluctuations on the scale of the Jeans length are still in the linear regime. Consequently, both the amplitude of dark-matter fluctuations on small scales and thermal smoothing affect the flux decrement distribution in a similar way. However, the b -parameter distribution of Voigt profile fits, obtained by deblending the absorption features into a sum of thermally broadened lines, is largely independent of the amount of small-scale power, but does depend strongly on the IGM temperature. The same is true for the two-point function of the flux and for the flux power spectrum on small scales. These three flux statistics are thus sensitive probes of the temperature of the IGM. We compare the values computed for our models and obtained from a HIRES spectrum of the quasar Q1422+231 and conclude that the IGM temperature at z ∼3.25 is fairly high, T ₀≳15 000 K. The flux decrement distribution of the observed spectrum is fitted well by that of a ΛCDM model with that temperature.     

Variation of the low-degree solar acoustic mode parameters over the solar cycle

VIRGO/SPM is a helioseismic sunphotometer on board SOHO that observes the disk-integrated sunlight irradiance at three different colors (red, green, and blue). The data obtained for SPM since the beginning of the SOHO mission, April 1996, to March 2001 have been used to study the differences of the p-mode parameters during the solar activity cycle. These time series have been divided in sub-series of 100 days, transformed to power spectra and averaged in sets of three to yield a total number of six averaged power spectra (around one per year). A new way of analyzing the power spectrum has been applied to the six power spectra of each color; it consists of fitting the whole p-mode spectrum at once with a unique background. The results for the frequencies, line widths, power, mode energy, energy rate fed in the mode and splittings along the activity cycle are found, compared and discussed.     

The galaxy power spectrum: precision cosmology from large-scale structure?

Published galaxy power spectra from the two-degree field galaxy redshift survey (2dFGRS) and Sloan Digital Sky Survey (SDSS) are not in good agreement. We revisit this issue by analysing both the 2dFGRS and SDSS Data Release 5 (DR5) catalogues using essentially identical techniques. We confirm that the 2dFGRS exhibits relatively more large-scale power than the SDSS, or, equivalently, SDSS has more small-scale power. We demonstrate that this difference is due to the r -band selected SDSS catalogue being dominated by more strongly clustered red galaxies, which have a stronger scale-dependent bias. The power spectra of galaxies of the same rest-frame colours from the two surveys match well. If not accounted for, the difference between the SDSS and 2dFGRS power spectra causes a bias in the obtained constraints on cosmological parameters which is larger than the uncertainty with which they are determined. We also found that the correction developed by Cole et al. to model the distortion in the shape of the power spectrum due to non-linear evolution and scale-dependent bias is not able to reconcile the constraints obtained from the 2dFGRS and SDSS power spectra. Intriguingly, the model is able to describe the differences between the 2dFGRS and the much more strongly clustered Luminous Red Galaxy (LRG) sample, which exhibits greater non-linearities. This shows that more work is needed to understand the relation between the galaxy power spectrum and the linear perturbation theory prediction for the power spectrum of matter fluctuations. It is therefore important to accurately model these effects to get precise estimates of cosmological parameters from these power spectra and from future galaxy surveys like Pan-STARRS, or the Dark Energy Survey, which will use selection criteria similar to the one of SDSS.     

The distribution of empirical periodograms: Lomb–Scargle and PDM spectra

The theoretical probability distributions of periodograms are derived for the assumed variance of noise. In practice, however, the variance is estimated from data and hence it is a random variable itself. The empirical periodograms , i.e. the periodograms normalized using the estimated variance, therefore follow a distribution different from that predicted by theory. We demonstrate that in general many empirical periodograms follow the beta distribution. In particular, as an example we consider a Lomb &38; Scargle (L–S) modified power spectrum with an exponential theoretical distribution. We derive its easy-to-use analytical empirical distribution. We demonstrate that the difference between the tails of the empirical and theoretical distributions is large enough to have a profound effect on the statistical significance of signal detections. The difference persists despite generally good asymptotic convergence of the distributions near their centres. Hence we argue that even for well-behaved statistics (e.g. L–S) one has to use our new empirical beta distributions rather than the theoretical ones. Our conclusions are illustrated by a realistic example. In the example we demonstrate a significant difference between the theoretical and empirical distributions. Additionally, we provide an example of conversion between analysis of variance (AOV), power-spectrum, PDM and χ² periodograms.     

Inversion of Thick-Target Bremsstrahlung Spectra from Nonuniformly Ionised Plasmas

The effects of non-uniform plasma target ionisation on the spectrum of thick-target HXR bremsstrahlung from a non-thermal electron beam are analysed. In particular the effect of the target ionisation structure on beam collisional energy losses, and hence on inversion of an observed photon spectrum to yield the electron injection spectrum, is considered and results compared with those obtained under the usual assumption of a fully ionised target.The problem is formulated and solved in principle for a general target ionisation structure, then discussed in detail for the case of a step function distribution of ionisation with column depth as an approximation to the sharp coronal–chromospheric step structure in solar flare plasmas. It is found that such ionisation structure has very dramatic effects on derivation of the thick-target electron injection spectrum F₀(E₀) as compared with the result F*₀(E ₀) obtained under the usual assumption of a fully ionised target: (a) Inferred F*₀ contain more electrons than F ₀ and in some cases include electrons at energies where none are actually present. Although the total (energy-integrated) beam fluxes in the two cases do not differ by a factor of more than A_ee/A_eH, the spectral shapes can differ greatly over finite energy intervals resulting in the danger of misleading results for total fluxes obtained by extrapolation. (b) The unconstrained mathematical solution for F₀ for any photon spectrum is never unique, while that for F*₀ is unique. When the physical constraint F₀ 0 is added, for some photon spectra solutions for F₀ may not exist or may not be unique. (This is not an effect of noise but of real analytic ambiguity.) (c) For data corresponding to F*₀ with a low-energy cut-off, or a cut-off or rapid enough exponential decline at high energies, a unique solution F₀ does exist and we obtain a recursive summation for its evaluation.Consequently, in future work on the inversion of HXR bremsstrahlung spectra it will be vital for algorithms to include the effects of target ionisation if spurious results on thick-target electron spectra are not to be inferred. Finally it is pointed out that the depth of the transition zone, and its evaporative evolution during flares may be derivable from its effect on the HXR spectrum.     

Numerical simulations of the Lyman α forest – a comparison of gadget-2 and enzo

We compare simulations of the Lyman α forest performed with two different hydrodynamical codes, gadget-2 and enzo . A comparison of the dark matter power spectrum for simulations run with identical initial conditions show differences of 1–3 per cent at the scales relevant for quantitative studies of the Lyman α forest. This allows a meaningful comparison of the effect of the different implementations of the hydrodynamic part of the two codes. Using the same cooling and heating algorithm in both codes, the differences in the temperature and the density probability distribution function are of the order of 10 per cent. The differences are comparable to the effects of box size and resolution on these statistics. When self-converged results for each code are taken into account, the differences in the flux power spectrum – the statistics most widely used for estimating the matter power spectrum and cosmological parameters from Lyman α forest data – are about 5 per cent. This is again comparable to the effects of box size and resolution. Numerical uncertainties due to a particular implementation of solving the hydrodynamic or gravitational equations appear therefore to contribute only moderately to the error budget in estimates of the flux power spectrum from numerical simulations. We further find that the differences in the flux power spectrum for enzo simulations run with and without adaptive mesh refinement are also of the order of 5 per cent or smaller. The latter require 10 times less CPU time making the CPU time requirement similar to that of a version of gadget-2 that is optimized for Lyman α forest simulations.     

Peaks in the cosmological density field: sensitivity to initial power spectrum, redshift distortions and galaxy halo occupation

We investigate the number density of maxima in the cosmological galaxy density field smoothed with a filter as a probe of clustering. In previous work it has been shown that this statistic is closely related to the slope of the linear power spectrum, even when the directly measured power spectrum is non-linear. In the present paper we investigate the sensitivity of the peak number density to various models with differing power spectra, including rolling index models, cosmologies with massive neutrinos and different baryon densities. We find that rolling index models which have given an improved fit to CMB/LSS (cosmic microwave background/large scale structure) data yield a ∼10 per cent difference in peak density compared to the scale invariant case. Models with 0.3 eV neutrinos have effects of similar magnitude and it should be possible to constrain them with data from current galaxy redshift surveys. Baryon oscillations in the power spectrum also give rise to distinctive features in the peak density. These are preserved without modification when measured from the peak density in fully non-linear N -body simulations. Using the simulations, we also investigate how the peak density is modified in the presence of redshift distortions. Redshift distortions cause a suppression of the number of peaks, largely due to fingers of God overlapping in redshift space. We find that this effect can be modelled by using a modification of the input power spectrum. We also study the results when the simulation density field is traced by galaxies obtained by populating haloes with a halo occupation distribution consistent with observations. The peak number density is consistent with that in the dark matter for filter scales  >4  h ⁻¹ Mpc  , for which we find good agreement with the linear theory predictions. In a companion paper we analyse data from the 2dF Galaxy Redshift Survey.     

On the formation and unfolding of pulse height distributions

Spacecraft measurements of X-ray or particle pulse height distributions have become increasingly accurate during the last fifteen years, and they will continue to do so. The present paper deals with the question how one can reconstruct original photon or particle spectra from measured pulse height distributions. The statistical aspects of the formation of pulse height distributions are investigated. A method is presented that allows for a reliable reconstruction of the original spectrum. Its essentials are the formulation and subsequent solution of a matrix equation connecting pulse height distribution with photon/particle spectrum; an error analysis of the reconstructed spectrum is given. The present method has two advantages over the usualχ ²-minimum method: It is able to recover more spectral detail and it requires less computing time. Finally, a numerical example is given.     

Structure and dynamics of galaxies with a low surface-brightness disc – I. The stellar and ionized-gas kinematics

Photometry and long-slit spectroscopy are presented for a sample of six galaxies with a low surface-brightness stellar disc and a bulge. The characterizing parameters of the bulge and disc components were derived by means of a two-dimensional photometric decomposition of the images of the sample galaxies. Their surface-brightness distribution was assumed to be the sum of the contribution of a Sérsic bulge and an exponential disc, with each component being described by elliptical and concentric isophotes of constant ellipticity and position angle. The stellar and ionized-gas kinematics were measured along the major and minor axes in half of the sample galaxies, whereas the other half was observed only along two diagonal axes. Spectra along two diagonal axes were obtained also for one of the objects with major and minor axis spectra. The kinematic measurements extend in the disc region out to a surface-brightness level  μ _R ≈ 24  mag arcsec⁻², reaching in all cases the flat part of the rotation curve. The stellar kinematics turns out to be more regular and symmetric than the ionized-gas kinematics, which often shows the presence of non-circular, off-plane and non-ordered motions. This raises the question about the reliability of the use of the ionized gas as the tracer of the circular velocity in the modelling of the mass distribution, in particular in the central regions of low surface-brightness galaxies.     

Turbulence in planetary occultations.: IV. Power spectra of phase and intensity fluctuations

Power spectra of phase and intensity scintillations during occultation by turbulent planetary atmospheres are significantly affected by the inhomogeneous background upon which the turbulence is superimposed. Such coupling is particularly pronounced in the intensity, where there is also a marked difference in spectral shape between a central and a grazing occultation. While the former has its structural features smoothed by coupling to the inhomogeneous background, such features are enhanced in the latter. Indeed, the latter power spectrum peaks around the characteristic frequency that is determined by the size of the free-space Fresnel zone and the ray velocity in the atmosphere; at higher frequencies strong fringes develop in the power spectrum. A confrontation between the theoretical scintillation spectra computed here and those calculated from the Mariner 5 Venus mission by R. Woo, A. Ishimaru, and W. B. Kendall (1974, J. Atmos. Sci.31, 1698–1706) is inconclusive, mainly because of insufficient statistical resolution. Phase and/or intensity power spectra computed from occultation data may be used to deduce characteristics of the turbulence and to distinguish turbulence from other perturbations in the refractive index. Such determinations are facilitated if observations are made at two or more frequencies (radio occultation) or in two or more colors (stellar occultation).     

The power spectrum of rich clusters of galaxies on large spatial scales

We present an analysis of the redshift-space power spectrum, P ( k ), of rich clusters of galaxies based on an automated cluster catalogue selected from the APM Galaxy Survey. We find that P ( k ) can be approximated by a power law, P ( k )∝ kⁿ , with n ≈−1.6 over the wavenumber range 0.04< k <0.1 h Mpc⁻¹. Over this range of wavenumbers, the APM cluster power spectrum has the same shape as the power spectra measured for optical and IRAS galaxies. This is consistent with a simple linear bias model in which different tracers have the same power spectrum as that of the mass distribution, but shifted in amplitude by a constant biasing factor. On larger scales, the power spectrum of APM clusters flattens and appears to turn over on a scale k ∼0.03 h Mpc⁻¹. We compare the power spectra estimated from simulated APM cluster catalogues with those estimated directly from cubical N -body simulation volumes, and find that the APM cluster survey should give reliable estimates of the true power spectrum at wavenumbers k ≳0.02 h Mpc⁻¹. These results suggest that the observed turnover in the power spectrum may be a real feature of the cluster distribution, and that we have detected the transition to a near-scale-invariant power spectrum implied by observations of anisotropies in the cosmic microwave background radiation. The scale of the turnover in the cluster power spectrum is in good agreement with the scale of the turnover observed in the power spectrum of APM galaxies.     

The structure of Galactic gas at high latitudes: The southern polar cap

We analyze the angular structure of the 21-cm interstellar neutral hydrogen emission at six and seven declinations in the northern (published previously) and southern polar caps of the Galaxy (Galactic latitudes from ?40° to ?90°), respectively, with an extent of 90° in right ascension. The RATAN-600 radio telescope has a beam width averaged over these regions of 2.′0×30′. One-dimensional power spectra for the angular distribution of interstellar neutral hydrogen emission were computed in each 6.3-km s^?1-wide spectral channel by using the standard Fast Fourier Transform (FFT) code and were smoothed over 1^h in right ascension. The Galactic latitude dependence of the mean parameters for the sky distribution of H I line emission at high latitudes was found to correspond to the distribution of gas in the form of a flat layer only in the northern region, while in the southern cap, the gas distribution is much less regular. In addition, the mean H I radial velocities are negative everywhere (?3.7±3.0 km s^?1 in the north and ?6.0±2.4 km s^?1 in the south). The power spectra of the angular fluctuations in the range of angular periods from 10′ to 6° appear as power laws. However, the spectral indices change greatly over the sky: from ?3 to ?1.2; on average, as the Galactic latitude increases and the H I column density decreases, the fluctuation spectrum of the interstellar gas emission becomes flatter. In the northern polar region, this behavior is much more pronounced, which probably stems from the fact that the gas column density in the south is generally a factor of 2 or 3 higher than that in the north. Therefore, the spectra are, on average, also steeper in the south, but the dependence on Galactic latitude is weaker. Using simulations, we show that the observed power-law spectrum of the H I emission distribution can be obtained in terms of not only a turbulent, but also a cloud model of interstellar gas if we use our previous spectra of the diameters and masses of H I clouds.     

Numerical study of the statistical properties of the lensing excursion angles

We present ray tracing simulations combined with sets of large N -body simulations. Experiments were performed to explore, for the first time, the statistical properties of fluctuations in angular separation of nearby light-ray pairs (the so-called lensing excursion angle) induced by weak lensing by large-scale structures. We found that the probability distribution function (PDF) of the lensing excursion angles is not simply Gaussian, but has an exponential tail. It is found, however, that the tail, or more generally the non-Gaussian nature of the PDF has no significant impact on the weak lensing of the cosmic microwave background (CMB). Moreover, we found that the variance in the lensing excursion angles predicted by the power spectrum approach is in good agreement with our numerical results. These results demonstrate the validity of using the power spectrum approach to compute lensing effects on the CMB.     

Angular power spectrum of CMB anisotropy from WMAP

The remarkable improvement in the estimates of different cosmological parameters in recent years has been largely spearheaded by accurate measurements of the angular power spectrum of cosmic microwave background (CMB) radiation. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel model-independent method for the estimation of CMB angular power spectrum from multi-frequency observations has been proposed and implemented on the first year WMAP (WMAP-1) data by Saha et al. [Saha, R., Jain, P., Souradeep, T., 2006. ApJL, 645, L89]. We review the results from WMAP-1 and also present the new angular power spectrum based on three years of the WMAP data (WMAP-3). Previous estimates have depended on foreground templates built using extraneous observational input to remove foreground contamination. This is the first demonstration that the CMB angular spectrum can be reliably estimated with precision from a self contained analysis of the WMAP data. The primary product of WMAP are the observations of CMB in 10 independent difference assemblies (DA) distributed over five frequency bands that have uncorrelated noise. Our method utilizes maximum information available within WMAP data by linearly combining DA maps from different frequencies to remove foregrounds and estimating the power spectrum from the 24 cross-power spectra of clean maps that have independent noise. An important merit of the method is that the expected residual power from unresolved point sources is significantly tempered to a constant offset at large multipoles (in contrast to the l² contribution expected from a Poisson distribution) leading to a small correction at large multipoles. Hence, the power spectrum estimates are less susceptible to uncertainties in the model of point sources.