Power Spectrum Index Research Articles

Kurtosis of large-scale cosmic fields

An attractive and simple hypothesis for the formation of large-scale structure is that it developed by gravitational instability from primordial fluctuations with an initially Gaussian probability distribution. Non-linear gravitational evolution drives the distribution away from the Gaussian form, generating measurable skewness and kurtosis even when the variance of the fluctuations is much smaller than unity. We use perturbation theory to compute the kurtosis of the mass density field and the velocity divergence field that arises during the weakly non-linear evolution of initially Gaussian fluctuations. We adopt an Einstein--de~Sitter universe for the perturbative calculations, and we discuss the generalization to a universe of arbitrary $\Omega$. We obtain semi-analytic results for the case of scale-free, power-law spectra of the initial fluctuations and final smoothing of cosmic fields with a Gaussian filter. We also give an exact analytical formula for the dependence of the skewness of these fields on the power spectrum index. We show that the kurtosis decreases with the power spectrum index, and we compare our more accurate results for the kurtosis to previous estimates from Monte Carlo integrations. We also compare our results to values obtained from cosmological N-body simulations with power-law initial spectra. Measurements of the skewness and kurtosis parameters can be used to test the hypothesis that structure in the universe formed by gravitational instability from Gaussian initial conditions.

Cosmic ray fluctuations in compressible turbulent medium

The influence of compressibility of the medium on cosmic ray (CR) fluctuations has been investigated. The CR transport equation has been used to obtain an equation for the second moment of CR particle density (correlation function of the particle density). It is shown that the effects due to the compressibility of the medium has an essential influence on CR fluctuations. The relations between CR power spectra and random velocity field have been determined. For the turbulence which is created by an ensemble of weak sound waves we have obtained the connection between the spectral indices of CR power spectra and the velocity field. It is shown that the spectral indices of CR power spectra and the velocity field of random sound waves coincide.

Recovering the inflationary potential.

A procedure is developed for the recovery of the inflationary potential over the interval that affects astrophysical scales (\ensuremath{\approx}1 Mpc to ${10}^{4}$ Mpc). The amplitudes of the scalar and tensor metric perturbations and their power-spectrum indices, which in principle can be inferred from large-angle CBR anisotropy and other cosmological data, determine the value of the inflationary potential and its first two derivatives. From these, the inflationary potential can be reconstructed in a Taylor series and the consistency of the inflationary hypothesis tested. Examples are presented, and the effect of observational uncertainties is discussed.

X-ray variability of active galactic nuclei - A universal power spectrum with luminosity-dependent amplitude

We present power-law model fits to the power spectra of 12 high-quality long look observations of AGNs from the EXOSAT data base. The AGNs concerned differ in X-ray luminosity L x over a range 10 4 . The results are consistent with all objects having a power spectrum index equal to the mean value α=1.55. There is no correlation with L x , suggesting that the power spectrum has little curvature over many decades of frequency. The mean slope is inconsistent with both standard shot-noise processes and traditional 1/f noise but close to the prediction of simple rotating hot spot models. The power spectrum amplitude shows large object-to-object scatter but varies systematically as L x -0.5 . This is inconsistent with any fixed-shape shot-noise model

Effects of long cosmic strings on the anisotropies of the cosmic background radiation

view Abstract Citations (14) References (34) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Effects of Long Cosmic Strings on the Anisotropies of the Cosmic Background Radiation Hara, Tetsuya ; Mahonen, Petri ; Miyoshi, Shigeru Abstract We have examined the effects of infinitely long cosmic strings on the anisotropies of the 2.7 K cosmic microwave background (CMB) radiation using a simplified model. It is assumed that N long cosmic strings are moving fast in each horizon volume during the e-folding times of the expansion of the universe. From the simulated anisotropies of the CMB over the whole sky, we have calculated the rms sky variation with a 10 deg FWHM Gaussian smoothing, the quadrupole moment, and the chi-squared test for the correlation functions. The comparison of the simulation with the COBE DMR results constrains the parameters. The effective power spectrum index is n = 1.1 +/- 0.5. Since the COBE results are well reproduced by our simulation, there remains a possibility that the CMB anisotropies detected by COBE are mainly due to cosmic strings. The characteristic feature for the cosmic string model is the discontinuities in the amplitude of CMB anisotropy. We discuss this as well as the constraint from smaller angles. Publication: The Astrophysical Journal Pub Date: September 1993 DOI: 10.1086/173088 Bibcode: 1993ApJ...414..421H Keywords: Cosmology; Radiation Distribution; Relic Radiation; String Theory; Anisotropy; Astronomical Models; Cosmic Background Explorer Satellite; Power Spectra; Space Radiation; COSMOLOGY: COSMIC MICROWAVE BACKGROUND; COSMIC STRINGS; COSMOLOGY: THEORY full text sources ADS |

Pickup protons and water ions at comet Halley: Comparisons with Giotto observations

A quasi‐linear diffusion model including both pitch angle and energy diffusion, adiabatic compression and convective motion with the solar wind flow has been used to investigate the cometary ion pickup process along the Sun‐comet line at comet Halley. The total pickup ion densities and magnetic turbulence spectrum levels observed by Giotto were used to constrain the quasi‐linear model. Comparisons of the model results were made with energetic ion distributions observed by instruments onboard the Giotto spacecraft. The observed power spectrum index of magnetic turbulence γ is about 2–2.5. However, our simulation shows that when γ was 2, the calculated proton distributions were much more isotropic than the observed ones; hence we have chosen γ = 2.5 in our study. Furthermore, we assumed that only about 5% of the total low frequency wave power propagates away from the comet. The numerical solutions of the quasi‐linear diffusion equations show that the isotropization of the pickup ion distribution, particularly at the pickup velocity, is not complete even close to the bow shock (but upstream), which agrees with the observations. The calculated and observed proton distributions are somewhat more isotropic than the water group ion distributions in the region far upstream of the shock, but the opposite is true near the bow shock. We find that given the observed turbulence level, quasi‐linear theory gives pickup ion energy distributions that agree with the observed ones quite well and easily produces energetic ions with energies up to hundreds of keV.

COBE versus cosmic strings. An analytical model

We construct a simple analytical model to study the effects of cosmic strings on the microwave background radiation. Our model is based on counting random multiple impulses inflicted on photon trajectories by the string network between the time of recombination and today. We construct the temperature auto-correlation function and use it to obtain the effective power spectrum index n, the RMS-quadrupole-normalized amplitude Q RMS-PS and the RMS temperature variation smoothed on small angular scales. For the values of the scaling solution parameters obtained by Bennett and Bouchet [Phys. Rev. D 41 (1990) 2408] and Allen and Shellard [Phys. Rev. Lett. 64 (1990) 119] we obtain n=1.14±0.5, Q RMS-PS =(4.55±1.5)Gμ and ( ΔT T ) RMS =5.5Gμ . Demanding consistency of these results with the COBE data leads to Gμ = (1.7 ± 0.7) × 10 −6 (where μ is the string mass per unit length), in good agreement with direct normalizations of μ from observations.

A tilted cold dark matter cosmological scenario

A new cosmological scenario based on CDM but with a power spectrum index of about 0.7-0.8 is suggested. This model is predicted by various inflationary models with no fine tuning. This tilted CDM model, if normalized to COBE, alleviates many problems of the standard CDM model related to both small-scale and large-scale power. A physical bias of galaxies over dark matter of about two is required to fit spatial observations.

Changes in the cosmic-ray power spectrum during solar flares

The power spectrum analyses of cosmic-ray neutron-monitor data at two different cutoff rigidity stations, Calgary (1.09 GV) and Lomnicky Stit (4.0 GV), exhibit similar changes in power spectral form in the frequency interval 10−5–10−3 Hz before and after the six solar flare events that occurred from January 1989 to June 1990. The power spectrum index n at both stations, which showed significantly lower values one day before the flare onset, indicated a sharp steepening of the spectral shape following the flare event. The change in the power spectrum is attributed to the redistribution of inhomogeneities near the sun, produced before the solar flares in which cosmic-ray particles are accelerated to high energies, to produce a ground level event.

Restriction of turbine blade vibrations in turbogenerators

A method for determining the effect and severity of turbine blade vibrations when subjected to balanced and unbalanced disturbance conditions is presented. An evaluation of severity is made using the index power spectrum density method and the results of representative studies are included to illustrate the effectiveness of the procedures adopted. Recommendations are made to depress blade vibration amplitudes in addition to the presentation of a feasible and easy to use analytical technique.

Characterizing solar flare high energy particles in near-Earth orbits

The high-latitude radiation environment at 840 km for the solar minimum period from December 1983 to October 1987 was measured, using a dosimeter on the DMSP/F7 satellite to characterize solar proton events and compare them to events from earlier periods near solar maximum. The solar proton spectra agree well. A method of characterizing the high-energy particles in solar proton events is proposed. It uses a power spectrum index and dose number that can be useful in specifying polar radiation environments for the design of spacecraft. Latitudinal cutoff levels for higher-energy (>35 MeV, >55 MeV, and >95 MeV) particles are also given for the solar proton event periods and compared to calculated cosmic ray cutoffs. >

Multifrequency spectra of day-time ionospheric amplitude scintillations near the dip equator

Power spectra of day-time amplitude scintillations on VHF and UHF signals from the geostationary satellite ATS-6 received at an equatorial station Ootacamund (magnetic dip 6°N) are studied in order to obtain information about long wavelength (≳ 100 m) irregularities generated in the equatorial electrojet plasma. Some of these spectra show Fresnel oscillations, which are usually absent for night-time amplitude power spectra, indicating thereby the presence of a thin layer of irregularities rather than a thick one, as is the case at night. We find that the drift speeds of irregularities estimated from the respective power spectra show expected variations with changes in the electrojet current strength. The high frequency asymptotes of power spectra yield a two-dimensional irregularity power spectrum index of 3.0 ± 0.4 over a wavelength range of approximately 60–800 m, which is close to the value 8/3 predicted by the unified theory of type I and type II irregularities in the equatorial electrojet for the so-called inertial range of wavelengths.