Perturbations of ionization fractions at the cosmological recombination epoch

The development of perturbations of number densities of ions and electrons during the recombination epoch is analysed. The equations for relative perturbations of ionization fractions were derived from the system of equations for accurate computation of the ionization history of the early Universe. It is shown that strong dependence of ionization and recombination rates on the density and temperature of plasma provides the significant deviations of amplitudes of ionization fractions relative to perturbations from those of baryon matter density adiabatic perturbations. Such deviations are most prominent for cosmological adiabatic perturbations of scales larger than the sound horizon at the recombination epoch. The amplitudes of relative perturbations of number densities of electrons and protons at the last scattering surface exceed by a factor of ≃5 the amplitude of the relative perturbation of baryons total number density: for helium ions this ratio reaches a value of ≃18. For subhorizon cosmological perturbations, these ratios appear to be essentially smaller and depend on oscillation phase at the moment of decoupling. These perturbations of number densities of ions and electrons at the recombination epoch do not contribute to the intrinsic plasma temperature fluctuations but cause the 'corrugation' of the last scattering surface in optical depth,  δ z _dec/( z _dec+ 1) ≈−δ_b/3  , at scales larger than the sound horizon. It may result in notable changes of pre-calculated values of the cosmic microwave background polarization pattern at several degrees of angular scales.     

Small-scale fluctuations of relic radiation

Perturbations of the matter density in a homogeneous and isotropic cosmological model which leads to the formation of galaxies should, at later stages of evolution, cause spatial fluctuations of relic radiation. Silk assumed that an adiabatic connection existed between the density perturbations at the moment of recombination of the initial plasma and fluctuations of the observed temperature of radiation δT/T=δ _?m /3 _?m . It is shown in this article that such a simple connection is not applicable due to:

1. The long time of recombination;
2. The fact that when regions withM<10¹⁵ M _⊙ become transparent for radiation, the optical depth to the observer is still large due to Thompson scattering;
3. The spasmodic increase of δ _?m/?m in recombination.

As a result the expected temperature fluctuations of relic radiation should be smaller than adiabatic fluctuations. In this article the value of δT/T arising from scattering of radiation on moving electrons is calculated; the velocity field is generated by adiabatic or entropy density perturbations. Fluctuations of the relic radiation due to secondary heating of the intergalactic gas are also estimated. A detailed investigation of the spectrum of fluctuations may, in principle, lead to an understanding of the nature of initial density perturbations since a distinct periodic dependence of the spectral density of perturbations on wavelength (mass) is peculiar to adiabatic perturbations. Practical observations are quite difficult due to the smallness of the effects and the presence of fluctuations connected with discrete sources of radio emission.     

The evolution of nonlinear hydrodynamical density fluctuations of the photon-plasma gas during the recombination era of the Universe

On the basis of the hydrodynamical equations of a two-component gas (photons and hydrogen with coupling via Thomson scattering) in the recombination era of the Universe (standard model), the evolution of the density perturbations up to second order are calculated. It is shown, that the generated second-order amplitudes of the density fluctuations of the matter reach values of the same order as the first-order amplitudes within only one tenth of the expansion time for fluctuations with wavelengths corresponding to 10⁷ M . Upper limits in the density fluctuations (for the gravitationally instable modes) up to which first-order calculations are valid, are given. This calculation indicates that the linear perturbation analysis is very restricted, especially at wavelengths near the lower limit of the Jeans length.The linear analysis would be a good approximation only for density fluctuations of the matter with the density contrast less than 10^–5–10^–4 at the recombination era. Therefore, a nonlinear analysis which is not based on a perturbation series is required for studying the evolution of the density perturbations, because for this we need a density contrast of 10^–2–10^–3 at the end of the recombination era.     

Filamentation Instability of Nonlinear Alfvén Waves and Plasma Heating associated with Recombination Effect

We investigate plasma heating associated with the effect of recombination and the filamentation instability of Alfvén waves propagating along homogeneous magnetic field in low-beta plasmas, by using an MHD simulation code. The linear instability of Alfvén waves leading to the filamentation is investigated by imposing small density perturbations across a magnetic field. We show results of the nonlinear stage of the above filamentation instability and the plasma heating through a two-dimensional simulation. It is shown that the plasma heating is caused by localized heating and whole heating, which are associated with the filamentation instability and the effect of recombination, respectively. We discuss the implication of these results for plasma heating processes observed in the chromosphere of the Sun.     

The origin and characteristic scale of galaxies

In this paper, we investigate the influence of the massive neutrino on the early evolution of adiabatic perturbations in the Universe. It is shown that if the neutrino has a non-zero rest mass, the perturbations that are approximately in a critical, stable state (for the Jeans instability) before the recombination of hydrogen will possibly grow into a kind of astronomical object which will have a preferred scale after the recombination. A reasonable estimate of the order of magnitude shows that such objects seem to be corresponding to the observed galaxies.     

Forward Modelling of Coronal Intensity Perturbations

In this paper, forward modelling is used to investigate the relation between given temperature and density perturbations and the resulting (synthesised) intensity perturbations, as would be observed by, e.g., TRACE and EIS (onboard Hinode). Complex and highly non-linear interactions between the components which make up the intensity (density, ionisation balance and emissivity) mean that it is non-trivial to reverse this process, i.e., obtain the density and temperature perturbations associated with observed intensity oscillations. In particular, it is found that the damping rate does not often ‘survive’ the forward modelling process, highlighting the need for a very careful interpretation of observed (intensity) damping rates. With a few examples, it is demonstrated that in some cases even the period of the oscillations can be altered and that it is possible for two different sets of input temperature and density to lead to very similar intensities (the well-known ‘ill-posed’ inversion process).     

Properties of dispersive Alfvén waves: 2. Kinetics (finite and high density plasmas)

The work is devoted to the study of the behavior of dispersive Alfvén waves in astrophysical plasma of finite and high pressure. All the main wave characteristics were obtained, namely, the dispersion, fading, polarization, density perturbations, and charge density perturbations. The effect of the parameters of the space environment on the behavior and properties of dispersive Alfvén waves was analyzed. The wave behavior in finite and high-pressure plasmas is shown to differ appreciably from the behavior in very low, intermediate, and low-pressure plasmas.     

Detecting ionized bubbles in redshifted 21-cm maps

Linear transient phenomena induced by flow non-normality in thin self-gravitating astrophysical discs are studied using the shearing sheet approximation. The considered system includes two modes of perturbations: vortex and (spiral density) wave. It is shown that self-gravity considerably alters the vortex mode dynamics; its transient (swing) growth may be several orders of magnitude stronger than in the non-self-gravitating case and two to three times larger than the transient growth of the wave mode. Based on this finding, we comment on the role of vortex mode perturbations in a gravitoturbulent state. We also describe the linear coupling of the perturbation modes, caused by the differential character of disc rotation. The coupling is asymmetric: vortex mode perturbations are able to excite wave mode perturbations, but not vice versa. This asymmetric coupling lends additional significance to the vortex mode as a participant in spiral density waves and shock manifestations in astrophysical discs.     

Gravitational stability of dark energy in galaxies and clusters of galaxies

We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark matter and dark energy, which interact only gravitationally, along with the perturbations of metric in a static world with background Minkowski metric. It was shown that quintessential and phantom dark energy in the static world of galaxies and clusters of galaxies is gravitationally stable and can only oscillate by the influence of self-gravity. In the gravitational field of dark matter perturbations, it is able to condense monotonically, but the amplitude of density and velocity perturbations on all scales remains small. It was also illustrated that the “accretion” of phantom dark energy in the region of dark matter overdensities causes formation of dark energy underdensities-the regions with negative amplitude of density perturbations of dark energy.     

Early star formation and galaxy formation triggered by the evolution of large-scale density perturbations

The evolution of small-scale density perturbations on the background of increasing large-scale perturbations of supercluster size will be considered. In the case that the characteristic length scales of both perturbation modes differ significantly, the interaction between both modes has to be taken into account already within lowest order of approximation. It will be shown that in this case an effective amplification for the smaller-scale perturbations occurs. For these perturbations the characteristic times of evolution decreases in dependence on the considered mass-scales more or less rapidly. Therefore, the growth of adiabatic density perturbations on mass-scales up to galaxy masses seems to be triggered by the density evolution of superclusters which the smaller-mass perturbations are embedded in. A model for the formation of observed condensed matter distribution will be proposed.     

Generation of low-frequency magnetic field disturbances in coronal loops by proton and electron beams

We consider the generation of low-frequency magnetic field disturbances in coronal loops when low density proton and electron beams propagate in them. Two mechanisms of low-frequency magnetic field perturbation generation are analyzed. The first mechanism is concerned with the longitudinal current generated by charged particles’ beams moving in the loop. It is shown that this mechanism of the Alfvén waves’ generation can lead to development of low-frequency perturbations even if the currents are very weak. It can facilitate the reconnection of magnetic fields and flare development. The second mechanism is not concerned with currents propagating in the coronal loop. It is shown that, in this case, the proton beams can cause an instability with significantly lower values of beam density. We found increments and criteria of the development of instabilities. Not only Alfvén-type perturbations can be generated as a result of development of those instabilities but also kinetic Alfvén-type perturbations can be generated.     

The growth of linear perturbations in generic defect models for structure formation

We study the growth of linear perturbations induced by a generic causal scaling source as a function of the cosmological parameters h ,     and     . We show that for wavenumbers k ≳0.01  h  Mpc⁻¹ the spectrum of density and velocity perturbations scales in a similar way to that found in inflationary models with primordial perturbations. We show that this result is independent of the more-or-less incoherent nature of the source, the small-scale power spectrum of the source and of deviations from scaling that naturally occur at late times if     .     

The electron temperature and density in interstellar medium by using carbon radio recombination line observations

The intensities of carbon radio recombination lines (RRL’s) are definedallowing for the effect of dielectronic-like recombination. The rate ofdielectronic-like recombination is calculated as functions of line number,electron density and temperature accurate to 0.05. Following from the balanceequation solutions for populations, the RRL intensities are analytically foundby the method of successive approximations to an accuracy of 0.15. Theobservations of carbon RRL’s are analyzed toward Cassiopeia A. The averageelectron temperature, density, expanded CII region lengths and inaccuraciesare found with the experimental values of RRL widths and intensities.     

Estimation of lunar and solar tides in the Earth’s thermosphere from density measurements by the CACTUS microaccelerometer

The densities measured by the CACTUS microaccelerometer at altitudes from 270 to 600 km are used to analyze the effect of tidal perturbations in the Earth’s thermosphere caused by the gravitational attraction of the Moon and the Sun. These tidal perturbations are considered a priori small and are not taken into account in modern atmospheric density models. The residuals between the densities measured by the CACTUS microaccelerometer and calculated by models are analyzed, and the density variations correlating with variations of the zenith angles from the Moon to the center of the Earth to the satellite and from the Sun to the center of the Earth to the satellite are found at altitudes from 270 to 600 km. The amplitude of the perturbations revealed in the study grows with height. The phase of the tidal perturbations also varies with height. The amplitude of the density variations is about 30% at 270–320 km and increases to 80% at 520–570 km. The results agree with a priori theoretical estimates obtained for tidal motion of gaseous matter with a variable density.     

The strength of the lunar lithosphere

A self-gravitating, elastic, spherical thick shell model is used to derive the present state of the lateral variations of density and stress differences within the lunar lithosphere. The model is allowed to deform under the load of an initial surface topography and internal density distribution, such that the resulting deformed body gives rise to the observed surface topography and gravity specified by the spherical harmonics of degree up to 70. Two main models are considered, Model A and Model B, with elastic lithospheres of thickness 300 and 210 km, respectively. Model A displays density perturbations of generally less than ±200 kg/m³ within the crustal layers, reducing rapidly to less than ±20 kg/m³ at the base of the lithosphere. The density perturbations in Model B are similar in the crust and marginally higher at the base of the lithosphere. The major stress differences in the mantle are associated with the mascon basins and are found to reach maximums of 8-10 MPa within the lower lithosphere (150-270 km) of Model A and maximums of 12-16 MPa at 150 to 180 km depth for Model B. A moderate correlation exists between the modeled stress distributions and shallow moonquake epicenters. However, the overall results of this study imply that other remnant stresses, due to processes other than density perturbations, exist and play a critical role in the large shallow moonquakes.     

The growth of density perturbations in the Lemaître universe

The rate of growth of density perturbations in certain Lemaître universes has been investigated using the differential equation derived by Bonnor. The perturbations that must be postulated at decoupling are not significantly different from those required in the conventional zero-pressure Friedmann-Lemaître models.     

Periodicity in the distribution of quasar redshifts and density perturbation in the early universe

We made a power spectrum analysis on the quasar emission redshift distribution, and further confirmed the existence of periodicity in respect of the quantity x = F_(z,qo) defined at (8).The existence of this periodicity does not mean that the quasar redshift is non-cosmological, for it can be interpreted as a remnant of density (acoustic) perturbations in the early big-bang universe. For this model, we made a number of tests. We found: 1) the ratio of periodic to non-periodic components falls as the sample size increases; 2) the periodicity should be more marked for quasars in one region of the sky than for all quasars, and 3) the Jeans wavelength before the recombination epoch determines the length of the period. Using this model we also found that qo > 0.5, lending further support to the conclusion reached by other means that the universe may be closed.     

The growth of density perturbations in Friedmann model universes with a decoupled radiation field

We examine the linear growth of density perturbations in homogeneous isotropic (Friedmann) model universes, including the effect of a decoupled radiation pressure field in the modelling. Amplification factors for density perturbations in all models are derived numerically, and it is shown that the effect of radiation pressure is to decelerate the growth of such condensations, thus requiring larger inhomogeneities to be produced at radiation decoupling in order to produce protogalaxies.     

A theory for expanding,large-scale,isolated, spherically-symmetric density perturbations with null peculiar velocity field

Exact theory for expanding density perturbations under the following assumptions: (i) Friedmann universes made of dust only; (ii) spherically-symmetric perturbations (iii) isolated perturbations; (iv) null peculiar velocity field; is reviewed and extended. The overdensity equation is derived and the related solution is determined concerning both mean overdensity and local overdensity, and including both the growing and the decreasing mode, in terms of non-dimensional variables normalized to the initial configuration. A first-order and zero-order approximation to the exact theory is also performed in view of applications to specific problems, e.g., the acquisition of angular momentum by tidal torques. The idealized case presented here makes a necessary reference in dealing with more general situations involving both analytical and numerical approaches.     

Influence of the Earth's rotation and of possible perturbations,on the exobase and exospheric hydrogen densities

In this study, we try to refine the relation existing between the exobase temperature and density distributions of atomic hydrogen around the Earth (assuming that the zero net ballistic flux condition is satisfied all over the critical level). We find essentially that neither local heating in high latitude regions, nor the addition of proton fluxes around the Earth, induce large perturbations in the equatorial density distribution (less than 10 per cent). On the other hand, certain local heating can give large perturbations in the global density distribution (more than 50 per cent).The effect of the Earth's rotation is also studied. We find that at the exobase the density distribution of atomic hydrogen lags about one hour behind the temperature distribution. At higher altitudes this time lag increases, reaching 5–6 hr at 20 Earth radii.We show also that, due to a density inversion which takes place at 2 Earth radii, if the minimum of density at the exobase is on the dayside, above 2 Earth radii, a maximum of density is then on the dayside when going higher, due to the rotational effect, that density maximum shifts towards the evening, reaching early parts of the night at 20 Earth radii.