The difference PDF of 21-cm fluctuations: a powerful statistical tool for probing cosmic reionization

A new generation of radio telescopes are currently being built with the goal of tracing the cosmic distribution of atomic hydrogen at redshifts 6–15 through its 21-cm line. The observations will probe the large-scale brightness fluctuations sourced by ionization fluctuations during cosmic reionization. Since detailed maps will be difficult to extract due to noise and foreground emission, efforts have focused on a statistical detection of the 21-cm fluctuations. During cosmic reionization, these fluctuations are highly non-Gaussian and thus more information can be extracted than just the one-dimensional function that is usually considered, i.e. the correlation function. We calculate a two-dimensional function that if measured observationally would allow a more thorough investigation of the properties of the underlying ionizing sources. This function is the probability distribution function (PDF) of the difference in the 21-cm brightness temperature between two points, as a function of the separation between the points. While the standard correlation function is determined by a complicated mixture of contributions from density and ionization fluctuations, we show that the difference PDF holds the key to separately measuring the statistical properties of the ionized regions.     

Suppression of resonant field line oscillations by a turbulent background

Stochastic fluctuations of the magnetospheric plasma and background magnetic field, especially intense during geomagnetically active periods, can provide an additional mechanism of damping of Alfvén field line oscillations. To quantify this hypothesis, we consider a driven Alfvén field line resonator with stochastic fluctuations of the Alfvén resonant frequency. This problem is first considered analytically for a low level of fluctuations, then a more general numerical approach is introduced. The results of analytical calculations and numerical modeling both indicate the deterioration of resonant properties of the resonator owing to stochastic background fluctuations.     

Fluctuations of electron precipitation to the dayside auroral zone modulated by compression and expansion of the magnetosphere

Concurrent variations of CNA fluctuations and geomagnetic fluctuations are classified into Type 1 (substorm-type), Type 2 (Pc5-type), and Type 3 which is the object of the present study. Type 3 apparently has peculiar characteristics in that CNA fluctuations at a certain auroral-zone station show a pronounced positive correlation with magnetic fluctuations at distant low-latitude stations. The magnetic fluctuations of this type are identified to generalized Si which tends to take place much more frequently than the so-called Si. The CNA fluctuations of this type are found to take place on the dayside auroral zone only when preceded by a magnetic substorm on the night side. Considering the change of the growth rate of electron cyclotron instability and enhancement of pitch angle diffusion due to the change of magnetic field intensity, the following model is proposed to explain the occurrence mechanism of Type 3 concurrent variations. The CNA fluctuations take place only when two conditions are satisfied; generation of the accelerated electrons in association with substorm onset and modulation of the precipitation of the electrons by compression and expansion of the magnetosphere, in other words, by generalized Si.     

21-cm fluctuations from inhomogeneous X-ray heating before reionization

Many models of early structure formation predict a period of heating immediately preceding reionization, when X-rays raise the gas temperature above that of the cosmic microwave background. These X-rays are often assumed to heat the intergalactic medium (IGM) uniformly, but in reality will heat the gas more strongly closer to the sources. We develop a framework for calculating fluctuations in the 21-cm brightness temperature that originate from this spatial variation in the heating rate. High-redshift sources are highly clustered, leading to significant gas temperature fluctuations (with fractional variations ∼40 per cent, peaking on   k ∼ 0.1 Mpc⁻¹  scales). This induces a distinctive peak-trough structure in the angle-averaged 21-cm power spectrum, which may be accessible to the proposed Square Kilometre Array. This signal reaches the ∼10 mK level, and is stronger than that induced by Lyα flux fluctuations. As well as probing the thermal evolution of the IGM before reionization, this 21-cm signal contains information about the spectra of the first X-ray sources. Finally, we consider disentangling temperature, density and Lyα flux fluctuations as functions of redshift.     

Measuring the power spectrum of density fluctuations at intermediate redshift with X-ray background observations

The precision of intensity measurements of the extragalactic X-ray background (XRB) on an angular scale of about a degree is dominated by spatial fluctuations caused by source confusion noise. X-ray source counts at the flux level responsible for these fluctuations, ∼10⁻¹² erg cm⁻² s⁻¹, will soon be accurately measured by new missions, and it will then be possible to detect the weaker fluctuations caused by the clustering of the fainter, more distant sources which produce the bulk of the XRB. We show here that measurements of these excess fluctuations at the level of (Δ I/I )∼2×10⁻³ are within reach, improving by an order of magnitude on present upper limits. Since it is likely that most (if not all) of the XRB will be resolved into sources by AXAF , subsequent optical identification of these sources will reveal the X-ray volume emissivity in the Universe as a function of redshift. With these ingredients, all-sky observations of the XRB can be used to measure the power spectrum (PS) of the density fluctuations in the Universe at comoving wavevectors k _c∼0.01–0.1 Mpc⁻¹ at redshifts where most of the XRB is likely to originate ( z ∼1–2) with a sensitivity similar to, or better than, the predictions from large-scale structure theories. A relatively simple X-ray experiment, carried out by a large-area proportional counter with a 0.5–2 deg² collimated field of view scanning the whole sky a few times, would be able to determine the PS of the density fluctuations near its expected peak in wavevector with an accuracy better than 10 per cent.     

Large density fluctuations in the martian ionosphere as observed by the Mars Express radar sounder

The MARSIS (Mars Advanced Radar for Subsurface and Ionosphere Sounding) instrument on the Mars Express spacecraft provides both local and remote measurements of electron densities and measurements of magnetic fields in the martian ionosphere. The density measurements show a persistent level of large fluctuations, sometimes as much as a factor of three or more at high altitudes. Large magnetic field fluctuations are also observed in the same region. The power spectrums of both the density and magnetic field fluctuations have slopes on a log-log plot that are consistent with the Kolmogorov spectrum for isotropic fluid turbulence. The fractional density fluctuation, Δn_e/n_e, of the turbulence increases with altitude, and reaches saturation, Δn_e/n_e ∼ 1, at an altitude of about 400 km, near the nominal boundary between the ionosphere and the magnetosheath. The fluctuations are usually so large that a well-defined ionopause-like boundary between the ionosphere and the solar wind is seldom observed. Of mechanisms that could be generating this turbulence, we believe that the most likely are (1) solar wind pressure perturbations, (2) an instability in the magnetosheath plasma, such as the mirror-mode instability, or (3) the Kelvin-Helmholtz instability driven by velocity shear between the rapidly flowing magnetosheath and the ionosphere.     

A model for solar oscillations at cm and mm wavelengths

It is suggested that large scale oscillations of the Sun give rise to the periodic fluctuations observed in the quiet Sun at radio wavelengths. These fluctuations would be most readily observed from regions where there is a large gradient of electron temperature with electron density, and are thus more readily observed at cm wavelengths than at millimetre wavelengths.     

Long-term measurements of 36Cl to investigate potential solar influence on the decay rate

Recently, Jenkins et al. [6] reported on fluctuations in the detected decay events of ³⁶Cl which were measured with a Geiger–Müller counter. Experimental data of ³²Si measured by means of an end-window gas-flow proportional counter at the Brookhaven National Laboratory show similar periodicity, albeit a different amplitude. Jenkins et al. interpret the fluctuations as evidence of solar influence on the decay rates of beta-decaying radionuclides.In this work, liquid scintillation counting was used to check for potential variations in the ³⁶Cl decay rates. A custom-built counter with three photomultiplier tubes was used. In contrast to commercial counters, the relevant parameters of our system are well controlled and the discrimination threshold and HV setting can be adjusted and checked. The experimental data were analyzed by means of the triple-to-double coincidence ratio (TDCR) method which is a primary method for activity determination. Thus, our results do not depend on any other standard or reference source.Our data show fluctuations which are by more than one order of magnitude lower than those seen in the experiment using a Geiger–Müller counter. More importantly, no oscillation could be identified. Interestingly, our data overlap in time with those from Jenkins et al. [6]. We do not observe the phase and amplitude as seen by Jenkins and conclude that the fluctuations are not due to solar influence. This also implies that the interpretation by Jenkins et al. is false.     

Thousand-Year Cycle Signals in Solar Activity

Long-term variations of solar activity closely relate to terrestrial phenomena. More and more people attach importance to studies of long-term fluctuations of solar variation. However, because direct observations of solar activity are available only for the past four centuries, such studies are few. In this work, using the wavelet technique, the author investigates long-term fluctuations of reconstructed sunspot number series covering the past 11 400 years, with emphasis on the thousand-year cycle signals of solar variation. The results show a thousand-year cycle in solar activity.     

Time variability of the Hei 10830 Å line profile

We have studied the time-dependent behaviour of the Hei 10830 Å line. These studies show that (i) the fluctuations of the line width are uncorrelated with the equivalent-width fluctuations and (ii) the autocorrelation curves for the equivalent-width fluctuations are broader than those for line-width fluctuations. These results could be interpreted as the signatures of the eruption of density inhomogeneities, like spicules, into the altitudes of formation of the Hei 10830 Å line.     

Smoothing of force functions and the fluctuation spectra of an open star cluster model

We perform the correlation and spectral analysis of phase-space density and potential fluctuations in a model of an open star cluster for various values of the smoothing parameter ? of the force functions in the equations of motion of cluster stars, and compute the mutual correlation functions for the fluctuations of potential U and phase-space density f of the cluster model at different clustercentric distances. We use the Fourier transform of the mutual correlation functions to compute the power spectra and dispersion curves of the potential and phase-space density fluctuations. The spectrum of potential fluctuations proves to be less complex than that of phase-space density fluctuations. The most powerful potential fluctuations are associated with phase-space density fluctuations, and their spectrum lies in the domain of low frequencies ν < 3/τ _v.r.; at intermediate and high frequencies (ν > 3/τ _v.r.), the contribution of potential fluctuations to those of the phase-space density is small or equal to zero (here τ _v.r. is the violent relaxation time scale of the cluster). We find a number of unstable potential fluctuations in the core of the cluster model (up to 30 pairs of fluctuations with different complex conjugate frequencies). We also find and analyze the dependences of the spectra and dispersion curves of phase-space density and potential fluctuations on ?. We find a “repeatability” (significant correlation) of the spectra at some values of parameter ?. The form of the dispersion curve is unstable against small variations of ?. We discuss the astrophysical applications of our results: the break-up in the cluster core of the phase-space density wave running from the cluster periphery toward its center into several waves with frequencies commensurable to that of the external (tidal) influence; emission and reflection of phase-space and potential waves near the cluster core boundary; possible wavelength and phase discretization of the phase-space and potential waves in the cluster model.     

Small-Scale Angular Fluctuations of Cosmic Background Radiation. Basic relations

A statistical treatment is given of small-scale angular fluctuations of cosmic background radiation propagating in FRIEDMANN models with Λ= o. It is assumed that the fluctuations arise from

• i the discrete nature of radiation sources;
• ii density inhomogeneities in continuously distributed radiating matter or from
• iii variable absorption along different light paths towards the observer.

The observable angular correlation function of the intensity fluctuations is expressed in terms of statistical measures of the sources of fluctuations. The rather general formulae are reduced as far as possible without specifying the frequency region.     

On the detection and utilization of gravity waves in airglow studies

We develop here theoretical relations between fluctuations of airglow brightness, fluctuations of temperature as revealed by airglow, and the atmospheric gravity waves that are believed to cause these fluctuations. We note and account for differences between our relations and those obtained by Krassovsky (1972, Ann. Geophys. 28, 739) and Weinstock (1978, J. geophys. Res. 83, 5175), correcting both of the latter in the process. We explicitly repudiate the need for a nonlinear treatment of O₂(¹Σ_g) emissions as it was asserted by Weinstock, one aspect of the nonlinear treatment he gave, and the conclusions he drew from that treatment, including, inter alia, the conclusion that temperature fluctuations carry more meaning as a diagnostic than do brightness fluctuations. Instead, we note the dependence of both types of fluctuation on variable gravity-wave parameters, which dependence can be applied to the study of gravity waves via airglow or of airglow via gravity waves. As a first step, we note the ability of the present analysis to account for certain observations of OH and O₂(¹Σ_g) emissions that have been, until now, inadequately or incorrectly explained, and we stress the importance of the proper measurement of parameters such as wave frequency and propagation speed if our own tentative explanations are to be put to the test and further progress is to be made.     

Modeling a Maunder minimum

We introduce on/off intermittency into a mean field dynamo model by imposing stochastic fluctuations in either the alpha effect or through the inclusion of a fluctuating electromotive force. Sufficiently strong small scale fluctuations with time scales of the order of 0.3–3 years can produce long term variations in the system on time scales of the order of hundreds of years. However, global suppression of magnetic activity in both hemispheres at once was not observed. The variation of the magnetic field does not resemble that of the sunspot number, but is more reminiscent of the ¹⁰Be record. The interpretation of our results focuses attention on the connection between the level of magnetic activity and the sunspot number, an issue that must be elucidated if long term solar effects are to be well understood. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Buoyancy waves in Pluto’s high atmosphere: Implications for stellar occultations

We apply scintillation theory to stellar signal fluctuations in the high-resolution, high signal/noise, dual-wavelength data from the MMT observation of the 2007 March 18 occultation of P445.3 by Pluto. A well-defined high wavenumber cutoff in the fluctuations is consistent with viscous-thermal dissipation of buoyancy waves (internal gravity waves) in Pluto’s high atmosphere, and provides strong evidence that the underlying density fluctuations are governed by the gravity-wave dispersion relation.     

Fluctuations in mid-latitude 6300 Å airglow and their relationship to F-region irregularities

Observations of fluctuations in the 6300 Å airglow emission at night have been studied using a tilting filter photometer. Spectral analysis of the fluctuations shows that at times the fluctuations are primarily due to wavelike disturbances with relatively well defined periods. At other times the spectrum of the fluctuations contains significant power only at long periods and there is a relatively sharp cut-off at the short period end. Most spectra are of these two types and are probably indicative of gravity waves. A third category is observed in which the spectra are of the form $\text{P∽?}{}^{\mathrm{?1.3}}$ Fewer spectra of this type are observed when the magnetic activity increases and the periods of spectral peaks observed changes with magnetic activity. The total power in the airglow fluctuations increases with K_p and the occurrence of spread F.     

Scintillations and Interstellar Lévy Flights

We present the new model for interstellar scintillations, which assumes that the electron density fluctuations causing the scintillations obey Lévy statistics rather than Gaussian statistics, as was thought previously. Our model explains the observed anomalous scaling of the signal time-width with respect to the pulsar distance, which remained a puzzle for more than 30 years.     

Some particularities affecting the movements of Jupiter's red spot

The fluctuations in longitude of Jupiter's Red Spot are discussed. The long term fluctuations show behaviour similar to the fluctuations of zonal circulations on the Earth from 1830–1950. The three-monthly fluctuations have a temporal connection with the inferior conjunction of Mercury 1963–1971. Solar activity may be the key to both phenomena.     

Quasinormal modes of scalar perturbation around a quantum-corrected Schwarzschild black hole

In this paper, we evaluate quasinormal modes (QNMs) of scalar perturbations around a quantum-corrected Schwarzschild black hole by using the third order Wentzel-Kramers-Brillouin (WKB) approximation method. The results show that due to the quantum fluctuations in the background of the Schwarzschild black hole, the QNMs of the black hole damp more slowly when increasing the quantum correction factor (a), and oscillate more slowly.     

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.