Baryon Fluid Research Articles

Stability of small-scale baryon perturbations during cosmological recombination

In this paper, we study small-scale fluctuations (baryon pressure sound waves) in the baryon fluid during recombination. In particular, we look at their evolution in the presence of relative velocities between baryons and photons on large scales ($k \sim 10^{-1} \ {\rm Mpc}^{-1}$), which are naturally present during the era of decoupling. Previous work concluded that the fluctuations grow due to an instability of sound waves in a recombining plasma, but that the growth factor is small for typical cosmological models. These analyses model recombination in an inhomogenous universe as a perturbation to the parameters of the homogenous solution. We show that for relevant wavenumbers $k\gtrsim 10^3\ {\rm Mpc}^{-1}$ the dynamics are significantly altered by the transport of both ionizing continuum ($h\nu>13.6$ eV) and Lyman-$\alpha$ photons between crests and troughs of the density perturbations. We solve the radiative transfer of photons in both these frequency ranges and incorporate the results in a perturbed three-level atom model. We conclude that the instability persists at intermediate scales. We use the results to estimate a distribution of growth rates in $10^{7}$ random realizations of large-scale relative velocities. Our results indicate that there is no appreciable growth; out of these $10^7$ realizations, the maximum growth factor we find is less than $\approx 1.2$ at wavenumbers of $k \approx 10^{3} \ {\rm Mpc}^{-1}$. The instability's low growth factors are due to the relatively short duration of the recombination epoch during which the electrons and photons are coupled.

Primordial magnetic fields from self-ordering scalar fields

A symmetry-breaking phase transition in the early universe could have led to the formation of cosmic defects. Because these defects dynamically excite not only scalar and tensor type cosmological perturbations but also vector type ones, they may serve as a source of primordial magnetic fields. In this study, we calculate the time evolution and the spectrum of magnetic fields that are generated by a type of cosmic defects, called global textures, using the non-linear sigma (NLSM) model. Based on the standard cosmological perturbation theory, we show, both analytically and numerically, that a vector-mode relative velocity between photon and baryon fluids is induced by textures, which inevitably leads to the generation of magnetic fields over a wide range of scales. We find that the amplitude of the magnetic fields is given by B∼10−9((1+z)/103)−2.5(v/mpl)2(k/Mpc−1)3.5/√N Gauss in the radiation dominated era for k≲ 1 Mpc−1, with v being the vacuum expectation value of the O(N) symmetric scalar fields. By extrapolating our numerical result toward smaller scales, we expect that B∼ 10−14.5((1+z)/103)1/2(v/mpl)2(k/Mpc−1)1/2/√N Gauss on scales of k≳ 1 Mpc−1 at redshift 0z≳ 110. This might be a seed of the magnetic fields observed on large scales today.

Baryonic matter perturbations in decaying vacuum cosmology

We consider the perturbation dynamics for the cosmic baryon fluid and determine the corresponding power spectrum for a Λ(t)CDM model in which a cosmological term decays into dark matter linearly with the Hubble rate. The model is tested by a joint analysis of data from supernovae of type Ia (SNIa) (Constitution and Union 2.1), baryonic acoustic oscillations (BAO), the position of the first peak of the anisotropy spectrum of the cosmic microwave background (CMB) and large-scale-structure (LSS) data (SDSS DR7). While the homogeneous and isotropic background dynamics is only marginally influenced by the baryons, there are modifications on the perturbative level if a separately conserved baryon fluid is included. Considering the present baryon fraction as a free parameter, we reproduce the observed abundance of the order of 5% independently of the dark-matter abundance which is of the order of 32% for this model. Generally, the concordance between background and perturbation dynamics is improved if baryons are explicitly taken into account.

Interacting photon–baryon fluid, warm dark matter, and the first acoustic peak

The Reduced Relativistic Gas (RRG) model was introduced by A. Sakharov in 1965 for deriving the cosmic microwave background (CMB) spectrum. It was recently reinvented by some of us to achieve an interpolation between the radiation and dust epochs in the evolution of the Universe. This model circumvents the complicated structure of the Boltzmann-Einstein system of equations and admits a transparent description of warm-dark-matter effects. It is extended here to include, on a phenomenological basis, an out-of-equilibrium interaction between radiation and baryons which is supposed to account for relevant aspects of pre-recombination physics in a simplified manner. Furthermore, we use the tight-coupling approximation to explore the influence of both this interaction and of the RRG warmness parameter on the anisotropy spectrum of the CMB. The predictions of the model are very similar to those of the {\Lambda}CDM model if both the interaction and the dark-matter warmness parameters are of the order of $10^{-4}$ or smaller. As far as the warmness parameter is concerned, this is in good agreement with previous estimations on the basis of results from structure formation.

NONLINEAR EVOLUTION OF COSMIC BARYON FLUID

Although the gravitational field in the universe is dominated by dark matter, observations show that the statistical properties of cosmic baryonic matter are significantly and systematically decoupled from that of the underlying dark matter. This is because the cosmic baryon fluid in highly nonlinear regime is in a state of fully developed turbulence, of which the velocity field consists of shocks, vortices and complex structures. This scenario provides a coherent explanation of various phenomena referring to the decoupling of the IGM from dark matter, including the log-Poisson non-Gaussianity of Ly-alpha transmitted flux fluctuations; turbulent broadening; abnormal scaling; baryon missing in halos etc.

Primordial magnetic fields generated by the non-adiabatic fluctuations at pre-recombination era

In the pre-recombination era, cosmological density fluctuations can naturally generate magnetic fields through Thomson scatterings. In previous studies, only the magnetic field generation from the initially- adiabatic fluctuations has been considered. Here we investigate the generation of cosmological magnetic fields sourced by the primordial non-adiabatic fluctuations based on the cosmological perturbation theory, using the tight-coupling approximations between photon and baryon fluids. It is found that the magnetic fields from the non-adiabatic fluctuations can arise at the first-order expansion of the tight coupling approximation. This result is in contrast to the case of adiabatic initial fluctuations, where the magnetic fields can be generated only at the second-order. In a general case where the primordial density perturbations contain small non-adiabatic fluctuations on the top of the dominant adiabatic ones, we show that the leading source of magnetic fields is given by the second-order coupling of the adiabatic and non-adiabatic fluctuations. We calculate the power spectrum of the generated magnetic fields when the non-adiabatic fluctuations have a blue power spectrum, which has been suggested by recent cosmological observations.

Suppression and spatial variation of early galaxies and minihaloes

We study the effect of the relative velocity of dark matter and baryonic fluids after the epoch of recombination on the evolution of the first bound objects in the early universe. Recent work has shown that, although relative motion of the two fluids is formally a second order effect in density, it has a dramatic impact on the formation and distribution of the first cosmic structures. Focusing on the gas content, we analyze the effect of relative velocity on the properties of halos over a wide range of halo masses and redshifts. We calculate accurately the linear evolution of the baryon and dark matter fluctuations, and quantify the resulting effect on halos based on an analytical formalism that has been carefully checked with simulations in the case with no relative velocity. We estimate the effect on the abundance of and gas fraction in early halos. We find that the relative velocity effect causes several changes: (i) the characteristic mass that divides gas-rich and gas-poor halos is increased by roughly an order of magnitude, from 2 10^4 Msun to about 2 10^5 Msun; (ii) this characteristic mass has a large scatter (full width at half maximum is ~ 1.5 10^5 Msun at z=20); (iii) the fraction of baryons in star-less gas minihalos is suppressed by a factor of 4 at z=20; (iv) the fraction of baryons in halos that can cool and form stars is suppressed by a factor of 1.5 at z=20; and (v) there are enhanced spatial variations of these various fractions.

Relative velocity of dark matter and baryonic fluids and the formation of the first structures

At the time of recombination, baryons and photons decoupled and the sound speed in the baryonic fluid dropped from relativistic, $\ensuremath{\sim}c/\sqrt{3}$, to the thermal velocities of the hydrogen atoms, $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}c$. This is less than the relative velocities of baryons and dark matter computed via linear perturbation theory, so we infer that there are supersonic coherent flows of the baryons relative to the underlying potential wells created by the dark matter. As a result, the advection of small-scale perturbations (near the baryonic Jeans scale) by large-scale velocity flows is important for the formation of the first structures. This effect involves a quadratic term in the cosmological perturbation theory equations and hence has not been included in studies based on linear perturbation theory. We show that the relative motion suppresses the abundance of the first bound objects, even if one only investigates dark matter haloes, and leads to qualitative changes in their spatial distribution, such as introducing scale-dependent bias and stochasticity. We further discuss the possible observable implications of this effect for high-redshift galaxy clustering and reionization.

Statistical and Dynamical Decoupling of the IGM from Dark Matter

Although the gravitational field in the universe is dominated by dark matter, cosmological observations show that the statistical properties of cosmic baryonic matter are significantly and systematically decoupled from that of the underlying dark matter. The dynamical reason of the decoupling is the difference of the nonlinear evolution of baryon fluid from that of collisionless dark matter. In highly nonlinear regime, the cosmic baryon fluid on scale free range evolves into the state of fully developed turbulence, of which the velocity field consists of shocks, vortices and complex structures. This scenario provides a coherent explanation of various phenomena referring to the statistical and dynamical decoupling of the IGM from dark matter.

Log-Poisson non-Gaussianity of Lyα transmitted flux fluctuations at high redshift

We investigate the non-Gaussian features of the IGM at redshift $z\sim 5 - 6$ using Ly$\alpha$ transmitted flux of quasar absorption spectra and cosmological hydrodynamic simulation of the concordance $\Lambda$CDM universe. We show that the neutral hydrogen mass density field and Ly$\alpha$ transmitted flux fluctuations possess all the non-Gaussian features predicted by the log-Poisson hierarchy, which depends only on two dimensionless parameters $\beta$ and $\gamma$, describing, respectively, the intermittence and singularity of the random fields. We find that the non-Gaussianity of the Ly$\alpha$ transmitted flux of quasars from $z=4.9$ to $z=6.3$ can be well reconstructed by the hydrodynamical simulation samples. Although the Gunn-Peterson optical depth and its variance underwent a significant evolution in the redshift range of $5 - 6$, the intermittency measured by $\beta$ is almost redshift-independent in this range. More interesting, the intermittency of quasar's absorption spectra on physical scales $0.1-1$ h$^{-1}$Mpc in redshift $5 - 6$ are found to be about the same as that on physical scales $1-10$ h$^{-1}$Mpc at redshifts $2 - 4$. Considering the Jeans length is less than 0.1 h$^{-1}$Mpc at $z\sim 5$, and $1$ h$^{-1}$Mpc at $z\sim 2$, these results imply that the nonlinear evolution in high and low redshifts will lead the cosmic baryon fluid to a state similar to fully developed turbulence. The log-Poisson high order behavior of current high redshift data of quasar's spectrum can be explained by uniform UV background in the redshift range considered. We also studied the log-Poisson non-Gaussianity by considering inhomogeneous background. With several simplified models of inhomogeneous background, we found the effect of the inhomogeneous background on the log-Poisson non-Gaussianity is not larger than 1-sigma.

Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

Scaling is an important measure of multi-scale fluctuation systems. Turbulence as the most remarkable multi-scale system possesses scaling over a wide range of scales. She-Leveque (SL) hierarchical symmetry, since its publication in 1994, has received wide attention. A number of experimental, numerical and theoretical work have been devoted to its verification, extension, and modification. Application to the understanding of magnetohydrodynamic turbulence, motions of cosmic baryon fluids, cosmological supersonic turbulence, natural image, spiral turbulent patterns, DNA anomalous composition, human heart variability are just a few among the most successful examples. A number of modified scaling laws have been derived in the framework of the hierarchical symmetry, and the SL model parameters are found to reveal both the organizational order of the whole system and the properties of the most significant fluctuation structures. A partial set of work related to these studies are reviewed. Particular emphasis is placed on the nature of the hierarchical symmetry. It is suggested that the SL hierarchical symmetry is a new form of the self-organization principle for multi-scale fluctuation systems, and can be employed as a standard analysis tool in the general multi-scale methodology. It is further suggested that the SL hierarchical symmetry implies the existence of a turbulence ensemble. It is speculated that the search for defining the turbulence ensemble might open a new way for deriving statistical closure equations for turbulence and other multi-scale fluctuation systems.

LOG-POISSON HIERARCHICAL CLUSTERING OF COSMIC NEUTRAL HYDROGEN AND Lyα TRANSMITTED FLUX OF QSO ABSORPTION SPECTRUM

we study, in this paper, the non-Gaussian features of the mass density field of neutral hydrogen fluid and the Ly-alpha transmitted flux of QSO absorption spectrum from the point-of-view of self-similar log-Poisson hierarchy. It has been shown recently that, in the scale range from the onset of nonlinear evolution to dissipation, the velocity and mass density fields of cosmic baryon fluid are extremely well described by the She-Leveque's scaling formula, which is due to the log-Poisson hierarchical cascade. Since the mass density ratio between ionized hydrogen to total hydrogen is not uniform in space, the mass density field of neutral hydrogen component is not given by a similar mapping of total baryon fluid. Nevertheless, we show, with hydrodynamic simulation samples of the concordance $\Lambda$CDM universe, that the mass density field of neutral hydrogen, is also well described by the log-Poisson hierarchy. We then investigate the field of Ly$\alpha$ transmitted flux of QSO absorption spectrum. Due to redshift distortion, Ly$\alpha$ transmitted flux fluctuations are no longer to show all features of the log-Poisson hierarchy. However, some non-Gaussian features predicted by the log-Poisson hierarchy are not affected by the redshift distortion. We test these predictions with the high resolution and high S/N data of quasars Ly$\alpha$ absorption spectra. All results given by real data, including $\beta$-hierarchy, high order moments and scale-scale correlation, are found to be well consistent with the log-Poisson hierarchy. We compare the log-Poisson hierarchy with the popular log-normal model of the Ly$\alpha$ transmitted flux. The later is found to yield too strong non-Gaussianity at high orders, while the log-Poisson hierarchy is in agreement with observed data.

Can a primordial magnetic field originate large-scale anomalies inWMAPdata?

Several accurate analyses of the cosmic microwave background (CMB) temperature maps from the Wilkinson Microwave Anisotropy Probe (WMAP) have revealed a set of anomalous results, at large angular scales, that appears inconsistent with the statistical isotropy expected in the concordance cosmological model Λcold dark matter. Because these anomalies seem to indicate a preferred direction in the space, here we investigate the signatures that a primordial magnetic field, possibly present in the photon–baryon fluid during the decoupling era, could have produced in the large-angle modes of the observed CMB temperature fluctuations maps. To study these imprints, we simulate Monte Carlo CMB maps, which are statistically anisotropic due to the correlations between CMB multipoles induced by the magnetic field. Our analyses reveal the presence of the north–south angular correlations asymmetry phenomenon in these Monte Carlo maps, and we use these information to establish the statistical significance of such phenomenon observed in WMAP maps. Moreover, because a magnetic field produces planarity in the low-order CMB multipoles, where the planes are perpendicular to the preferred direction defined by the magnetic field, we investigate the possibility that two CMB anomalous phenomena, namely the north–south asymmetry and the quadrupole–octopole planes alignment, could have a common origin. Our results, for large angles, show that the correlations between low-order CMB multipoles introduced by a sufficiently intense magnetic field, can reproduce some of the large-angle anisotropic features mapped in WMAP data. We also reconfirm, at more than 95 per cent CL, the existence of a north–south power asymmetry in the WMAP 5-yr data.

Scaling relation between Sunyaev–Zel’dovich effect and X-ray luminosity and scale-free evolution of cosmic baryon field

It has been revealed recently that, in the scale free range, i.e. from the scale of the onset of nonlinear evolution to the scale of dissipation, the velocity and mass density fields of cosmic baryon fluid are extremely well described by the self-similar log-Poisson hierarchy. As a consequence of this evolution, the relations among various physical quantities of cosmic baryon fluid should be scale invariant, if the physical quantities are measured in cells on scales larger than the dissipation scale, regardless the baryon fluid is in virialized dark halo, or in pre-virialized state. We examine this property with the relation between the Compton parameter of the thermal Sunyaev–Zel’dovich effect, y( r), and X-ray luminosity, L x ( r), where r being the scale of regions in which y and L x are measured. According to the self-similar hierarchical scenario of nonlinear evolution, one should expect that (1) in the y( r) − L x ( r) relation, y( r) = 10 A( r) [ L x ( r)] α( r) , the coefficients A( r) and α( r) are scale-invariant; (2) The relation y( r) = 10 A( r) [ L x ( r)] α( r) given by cells containing collapsed objects is also available for cells without collapsed objects, only if r is larger than the dissipation scale. These two predictions are well established with a scale decomposition analysis of observed data, and a comparison of observed y( r) − L x ( r) relation with hydrodynamic simulation samples. The implication of this result on the characteristic scales of non-gravitational heating is also addressed.

Non‐Gaussianity of the Cosmic Baryon Fluid: Log‐Poisson Hierarchy Model

In the nonlinear regime of cosmic clustering, the mass density field of the cosmic baryon fluid is highly non-Gaussian. It shows different dynamical behavior from collisionless dark matter. Nevertheless, the evolved field of the baryon fluid is scale-covariant in the range from the Jeans length to a few tens of h−1 Mpc, within which the dynamical equations and initial perturbations are scale free. We show that in the scale-free range, the non-Gaussian features of the cosmic baryon fluid, governed by the Navier-Stokes equation in an expanding universe, can be well described by a log-Poisson hierarchical cascade. The log-Poisson scheme is a random multiplicative process (RMP), which causes non-Gaussianity and intermittency even when the original field is Gaussian. The log-Poisson RMP contains two dimensionless parameters: β for the intermittency and γ for the most singular structure. All the predictions given by the log-Poisson RMP model, including the hierarchical relation, the order dependence of the intermittent exponent, the moments, and the scale-scale correlation, are in good agreement with the results given by hydrodynamic simulations of the standard cold dark matter model. The intermittent parameter β decreases slightly at low redshift and indicates that the density field of the baryon fluid contains more singular structures at lower redshifts. The applicability of the model is addressed.

CMB anisotropies at second-order II: analytical approach

We provide an analytical approach to the second-order cosmic microwave background(CMB) anisotropies generated by the non-linear dynamics taking place at last scattering.We study the acoustic oscillations of the photon–baryon fluid in the tight coupling limitand we extend at second order the Meszaros effect. We allow for a generic set of initialconditions due to primordial non-Gaussianity and we compute all of the additionalcontributions arising at recombination. Our results are useful to provide the fullsecond-order radiation transfer function at all scales necessary for establishing the level ofnon-Gaussianity in the CMB.

X‐Ray Emission of Baryonic Gas in the Universe: Luminosity‐Temperature Relationship and Soft‐Band Background

We study the X-ray emission of baryon fluid in the universe using the WIGEON cosmological hydrodynamic simulations. It has been revealed that cosmic baryon fluid in the nonlinear regime behaves like Burgers turbulence, i.e., the fluid field consists of shocks. Like turbulence in incompressible fluid, the Burgers turbulence plays an important role in converting the kinetic energy of the fluid to thermal energy and heats the gas. We show that the simulation sample of the Lambda CDMmodel without adding extra heating sources can fit well the observed distributions of X-ray luminosity versus temperature (L-X vs. T) of galaxy groups and is also consistent with the distributions of X-ray luminosity versus velocity dispersion (L-X vs. sigma). Because the baryonic gas is multiphase, the L-X-T and L-X-sigma distributions are significantly scattered. If we describe the relationships by power laws L-X alpha T-alpha LT and L-X alpha sigma(alpha LV), we find alpha(LT) > 2: 5 and alpha(LV) > 2:1. The X-ray background in the soft 0.5-2 keV band emitted by the baryonic gas in the temperature range 10(5) 50 (rho) over bar (dm) is generally clustered and discretely distributed. Therefore, almost all of the soft X-ray background comes from clustered sources, and the contribution from truly diffuse gas is probably negligible. This point agrees with current X-ray observations.

Low-Redshift Cosmic Baryon Fluid on Large Scales and She-Leveque Universal Scaling

We investigate the statistical properties of cosmic baryon fluid in the nonlinear regime, which is crucial for understanding the large-scale structure formation of the Universe. With the hydrodynamic simulation sample of the Universe in the cold dark matter model with a cosmological constant, we show that the intermittency of the velocity field of cosmic baryon fluid at redshift z = 0 in the scale range from the Jeans length to about 16 h(-1) Mpc can be extremely well described by She-Leveque's universal scaling formula. The baryon fluid also possesses the following features: (1) for volume weight statistics, the dissipative structures are dominated by sheets, and (2) the relation between the intensities of fluctuations is hierarchical. These results imply that the evolution of highly evolved cosmic baryon fluid is similar to a fully developed turbulence.

CMB anisotropy due to tangled magnetic fields in reionized models

Primordial tangled cosmological Magnetic Fields source rotational velocity perturbations of the baryon fluid, even in the post-recombination universe. These vortical modes inturn leave a characteristic imprint on the temperature anisotropy of the Cosmic Microwave Background (CMB), if the CMB photons can be rescattered after recombination. Observations from WMAP indicate that the Universe underwent a relatively early reionization (${z}_{ri}\ensuremath{\sim}15$), which does indeed lead to a significant optical depth for rescattering of CMB photons after the reionization epoch. We compute the resulting additional temperature anisotropies, induced by primordial magnetic fields in the post-recombination universe. We show that in models with early reionization, a nearly scale-invariant spectrum of tangled magnetic fields which redshift to a present value of ${B}_{0}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ Gauss, produce vector mode perturbations which in turn induce additional temperature anisotropy of about $0.3$ to $0.4$ $\ensuremath{\mu}$K over very small angular scales, with $l$ upto $\ensuremath{\sim}10000$ or so.

Inside charged black holes. I. Baryons

An extensive investigation is made of the interior structure of self-similar accreting charged black holes. In this, the first of two papers, the black hole is assumed to accrete a charged, electrically conducting, relativistic baryonic fluid. The mass and charge of the black hole are generated self-consistently by the accreted material. The accreted baryonic fluid undergoes one of two possible fates: either it plunges directly to the spacelike singularity at zero radius, or else it drops through the Cauchy horizon. The baryons fall directly to the singularity if the conductivity either exceeds a certain continuum threshold kappa_oo, or else equals one of an infinite spectrum kappa_n of discrete values. Between the discrete values kappa_n, the solution is characterized by the number of times that the baryonic fluid cycles between ingoing and outgoing. If the conductivity is at the continuum threshold kappa_oo, then the solution cycles repeatedly between ingoing and outgoing, displaying a discrete self-similarity reminiscent of that observed in critical collapse. Below the continuum threshold kappa_oo, and except at the discrete values kappa_n, the baryonic fluid drops through the Cauchy horizon, and in this case undergoes a shock, downstream of which the solution terminates at an irregular sonic point where the proper acceleration diverges, and there is no consistent self-similar continuation to zero radius. As far as the solution can be followed inside the Cauchy horizon, the radial direction is timelike. If the radial direction remains timelike to zero radius (which cannot be confirmed because the self-similar solutions terminate), then there is presumably a spacelike singularity at zero radius inside the Cauchy horizon, which is distinctly different from the vacuum solution for a charged black hole.