arXiv subjects

P. Valageas

Publications and source records attributed to P. Valageas.

36 records · Page 2Linked to original sources

arXiv2002

The phase-diagram of cosmological baryons

We investigate the behaviour of cosmological baryons at low redshifts $z<5$ after reionization through analytic means. In particular, we study the density-temperature phase-diagram which describes the history of the gas. We show how the location of the matter in this $(ρ,T)$ diagram expresses the various constraints implied by usual hierarchical scenarios. This yields robust model-independent results which agree with numerical simulations. The IGM is seen to be formed via two phases: a ``cool'' photo-ionized component and a ``warm'' component governed by shock-heating. We also briefly describe how the remainder of the matter is distributed over galaxies, groups and clusters. We recover the fraction of matter and the spatial clustering computed by numerical simulations. We also check that the soft X-ray background due to the ``warm'' IGM component is consistent with observations. We find in the present universe a baryon fraction of 7% in hot gas, 24% in the warm IGM, 38% in the cool IGM, 9% within star-like objects and, as a still un-observed component, 22% of dark baryons associated with collapsed structures, with a relative uncertainty no larger than 30% on these numbers.

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arXiv2002

Dynamics of gravitational clustering V. Subleading corrections in the quasi-linear regime

We investigate the properties of the standard perturbative expansions which describe the early stages of the dynamics of gravitational clustering. We show that for hierarchical scenarios with no small-scale cutoff perturbation theory always breaks down beyond a finite order $q_+$. Besides, the degree of divergence increases with the order of the perturbative terms so that renormalization procedures cannot be applied. Nevertheless, we explain that despite the divergence of these subleading terms the results of perturbation theory are correct at leading order because they can be recovered through a steepest-descent method which does not use such perturbative expansions. Finally, we investigate the simpler cases of the Zel'dovich and Burgers dynamics. In particular, we show that the standard Burgers equation exhibits similar properties. This analogy suggests that the results of the standard perturbative expansions are valid up to the order $q_+$ (i.e. until they are finite). Moreover, the first ``non-regular'' term of a large-scale expansion of the two-point correlation function should be of the form $R^{-2} σ^2(R)$. At higher orders the large-scale expansion should no longer be over powers of $σ^2$ but over a different combination of powers of 1/R. However, its calculation requires new non-perturbative methods.

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arXiv2002

Dynamics of gravitational clustering IV. The probability distribution of rare events

Using a non-perturbative method developed in a previous article (paper II) we investigate the tails of the probability distribution $P(ρ_R)$ of the overdensity within spherical cells. We show that our results for the low-density tail of the pdf agree with perturbative results when the latter are finite (up to the first subleading term), that is for power-spectra with $-3<n<-1$. Over the range $-1<n<1$ some shell-crossing occurs (which leads to the break-up of perturbative approaches) but this does not invalidate our approach. In particular, we explain that we can still obtain an approximation for the low-density tail of the pdf. This feature also clearly shows that perturbative results should be viewed with caution (even when they are finite). We point out that our results can be recovered by a simple spherical model but they cannot be derived from the stable-clustering ansatz in the regime $σ\gg 1$ since they involve underdense regions which are still expanding. Second, turning to high-density regions we explain that a naive study of the radial spherical dynamics fails. Indeed, a violent radial-orbit instability leads to a fast relaxation of collapsed halos (over one dynamical time) towards a roughly isotropic equilibrium velocity distribution. Then, the transverse velocity dispersion stabilizes the density profile so that almost spherical halos obey the stable-clustering ansatz for $-3<n<1$. We again find that our results for the high-density tail of the pdf agree with a simple spherical model (which takes into account virialization). Moreover, they are consistent with the stable-clustering ansatz in the non-linear regime. Besides, our approach justifies the large-mass cutoff of the Press-Schechter mass function (although the various normalization parameters should be modified).

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arXiv2002

Dynamics of gravitational clustering II. Steepest-descent method for the quasi-linear regime

We develop a non-perturbative method to derive the probability distribution $P(δ_R)$ of the density contrast within spherical cells in the quasi-linear regime. Indeed, since this corresponds to a rare-event limit a steepest-descent approximation can yield asymptotically exact results. We check that this is the case for Gaussian initial density fluctuations, where we recover most of the results obtained by perturbative methods from a hydrodynamical description. Moreover, we correct an error which was introduced in previous works for the high-density tail of the pdf. This feature, which appears for power-spectra with a slope $n<0$, points out the limitations of perturbative approaches which cannot describe the pdf $P(δ_R)$ for $δ_R \ga 3$ even in the limit $σ\to 0$. This break-up does not involve shell-crossing and it is naturally explained within our framework. Thus, our approach provides a rigorous treatment of the quasi-linear regime, which does not rely on the hydrodynamical approximation for the equations of motion. Besides, it is actually simpler and more intuitive than previous methods. Our approach can also be applied to non-Gaussian initial conditions.

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arXiv2002

Dynamics of gravitational clustering III. The quasi-linear regime for some non-Gaussian initial conditions

Using a non-perturbative method developed in a previous work (paper II), we derive the probability distribution $P(δ_R)$ of the density contrast within spherical cells in the quasi-linear regime for some non-Gaussian initial conditions. We describe three such models. The first one is a straightforward generalization of the Gaussian scenario. It can be seen as a phenomenological description of a density field where the tails of the linear density contrast distribution would be of the form $P_L(δ_L) \sim e^{-|δ_L|^{-α}}$, where $α$ is no longer restricted to 2 (as in the Gaussian case). We derive exact results for $P(δ_R)$ in the quasi-linear limit. The second model is a physically motivated isocurvature CDM scenario. Our approach needs to be adapted to this specific case and in order to get convenient analytical results we introduce a simple approximation (which is not related to the gravitational dynamics but to the initial conditions). Then, we find a good agreement with the available results from numerical simulations for the pdf of the linear density contrast for $δ_{L,R} \ga 0$. We can expect a similar accuracy for the non-linear pdf $P(δ_R)$. Finally, the third model corresponds to the small deviations from Gaussianity which arise in standard slow-roll inflation. We obtain exact results for the pdf of the density field in the quasi-linear limit, to first-order over the primordial deviations from Gaussianity.

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arXiv2001

Dynamics of gravitational clustering I. Building perturbative expansions

We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit calculation of the second-order terms which are shown to agree with the results obtained from the hydrodynamical description of the system. Then, we explain that this identity extends to all orders of perturbation theory and that the perturbative series actually diverge for hierarchical scenarios. However, since the collisionless Boltzmann equation provides the exact description of the dynamics (including the non-linear regime) these results may serve as a basis for a study of the non-linear regime. In particular, we derive a non-perturbative quadratic integral equation which explicitly relates the actual non-linear distribution function to the initial conditions (more precisely, to the linear growing mode). This allows us to write an explicit path-integral expression for the probability distribution of the exact non-linear density field.

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arXiv2001

Secondary CMB anisotropies from the kinetic SZ effect

We present an analytic model, based on previous works which tackled the reionization history of the universe, which allows us to describe the generation of the secondary CMB anisotropies due to the kinetic SZ effect. We take into account the "patchy pattern" of reionization (HII bubbles), the cross-correlations of these ionized regions, the small-scale fluctuations of the matter density field and the contribution from collapsed objects. For an open universe, we find that the power-spectrum $l(l+1)C_l/(2π)$ exhibits a plateau of height $10^{-13}$ in the range $10^3 < l < 10^6$. We find that for large wavenumbers $l > 10^4$ the signal is dominated by the contribution from collapsed halos while for $l < 10^4$ it is governed by the large-scale correlations of HII bubbles. This implies that one cannot discriminate reionization by stars from a quasar-driven scenario since the size of ionized regions never dominates the behaviour of the anisotropies. Moreover, the secondary CMB anisotropies arise from a broad range of redshifts (7.5<z<10 for the IGM and 0<z<7 for galactic halos). The signal expected in our model might bias the cosmological parameter estimation from CMB experiments such as Planck and could be detected by future mm-wavelength interferometers (e.g., ALMA).

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arXiv2001

Construction of the one-point PDF of the local aperture mass in weak lensing maps

We present a general method for the reconstruction of the one-point Probability Distribution Function of the local aperture mass in weak lensing maps. Exact results, that neglect the lens-lens coupling and departure form the Born approximation, are derived for both the quasilinear regime at leading order and the strongly nonlinear regime assuming the tree hierarchical model is valid. We describe in details the projection effects on the properties of the PDF and the associated generating functions. In particular, we show how the generic features which are common to both the quasilinear and nonlinear regimes lead to two exponential tails for $P(\Map)$. We briefly investigate the dependence of the PDF with cosmology and with the shape of the angular filter. Our predictions are seen to agree reasonably well with the results of numerical simulations and should be able to serve as foundations for alternative methods to measure the cosmological parameters that take advantage of the full shape of the PDF.

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arXiv2001

The redshift evolution of bias and baryonic matter distribution

We study the distribution of baryonic and luminous matter within the framework of a hierarchical scenario. Using an analytical model for structure formation which has already been checked against observations for galaxies, Lyman-$α$ clouds, clusters and reionization processes, we present its predictions for the bias of these objects. We describe its dependence on the luminosity (for galaxies or quasars) or the column density (for Lyman-$α$ absorbers) of the considered objects. We also study its redshift evolution, which can exhibit an intricate behaviour. These astrophysical objects do not trace the dark matter density field, the Lyman-$α$ forest clouds being undercorrelated and the bright galaxies overcorrelated, while the intermediate class of Lyman-limit systems is seen to sample the matter field quite well. We also present the distribution of baryonic matter over these various objects. We show that light does not trace baryonic mass, since bright galaxies which contain most of the stars only form a small fraction of the mass associated with virialized and cooled halos. We consider two cosmologies: a critical density universe and an open universe. In both cases, our results agree with observations and show that hierarchical scenarios provide a good model for structure formation and can describe a wide range of objects which spans at least the seven orders of magnitude in mass for which data exist. More detailed observations, in particular of the clustering evolution of galaxies, will constrain the astrophysical models involved.

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arXiv2000

Multiplicity Functions and X-ray emission of Clusters and Groups versus Galaxies and Quasars

We use a unified analytical formulation for the multiplicity functions of clusters and galaxies which is free from the cloud-in-cloud problem encountered in earlier approaches and well adapted to the description of the non-linear clustering features. It is especially suited to simultaneously describe rich clusters, groups and galaxies, consistently with the hierarchical picture of gravitational clustering and their evolution in time. Using a simple model for the X-ray luminosity (taking into account entropy considerations), we obtain the X-ray luminosity distribution of groups and clusters. Then, using the same formalism we derive the galaxy and quasar multiplicity functions. In particular, we show that the use of the standard Press-Schechter prescription leads to erroneous conclusions at low redshifts while our approach provides a reasonable agreement with observations in a natural fashion because it is able to distinguish galactic halos from groups or clusters. Thus, we obtain a global and consistent picture of the X-ray emissions from all structures. In particular, we show that future observations (e.g., from AXAF) could provide interesting information on galaxy evolution. Indeed, they will constrain the importance of a possible hot diffuse gaseous phase in galactic halos and they could reveal massive galaxies which are just being formed, through the X-ray emission of their cooling gas.

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arXiv2000

Statistical properties of the convergence due to weak gravitational lensing by non-linear structures

Density fluctuations in the matter distribution lead to distortions of the images of distant galaxies through weak gravitational lensing effects. This provides an efficient probe of the cosmological parameters and of the density field. In this article, we investigate the statistical properties of the convergence due to weak gravitational lensing by non-linear structures (i.e. we consider small angular windows $θ\la 1'$). Previous studies have shown how to relate the second and third order moments of the convergence to those of the density contrast while models based on the Press-Schechter prescription provide an estimate of the tail of $P(κ)$. Here we present a method to obtain an estimate of the full p.d.f. of the convergence $P(κ)$. It is based on a realistic description of the density field which applies to overdense as well as underdense regions. We show that our predictions agree very well with the results of N-body simulations for the convergence. This could allow one to derive the cosmological parameters $(Ω_m,Ω_Λ)$ as well as the full p.d.f. $P(δ_R)$ of the density contrast itself in the non-linear regime from observations. Hence this gives a very powerfull tool to constrain scenarios of structure formation.

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arXiv2000

Weak gravitational lensing effects on the determination of $Ω_m$ and $Ω_Λ$ from SNeIa

In this article we present an analytic calculation of the probability distribution of the magnification of distant sources due to weak gravitational lensing from non-linear scales. We use a realistic description of the non-linear density field, which has already been compared with numerical simulations. Then, we can directly express the p.d.f. $P(μ)$ of the magnification in terms of the p.d.f. of the density contrast realized on non-linear scales (typical of galaxies) where the local slope of the initial linear power-spectrum is $n=-2$. We recover the behaviour seen by numerical simulations: $P(μ)$ peaks at a value slightly smaller than the mean $<μ>=1$ and it shows an extended large $μ$ tail (as described in another article our predictions also show a good quantitative agreement with results from N-body simulations for a finite smoothing angle). Then, we study the effects of weak lensing on the derivation of the cosmological parameters from SNeIa. We show that the inaccuracy introduced by weak lensing is not negligible: $ΔΩ_m \ga 0.3$ for two observations at $z_s=0.5$ and $z_s=1$. However, observations can unambiguously discriminate between $Ω_m=0.3$ and $Ω_m=1$. Moreover, in the case of a low-density universe one can clearly distinguish an open model from a flat cosmology (besides, the error decreases as the number of observed SNeIa increases). Since distant sources are more likely to be ``demagnified'' the most probable value of the observed density parameter $Ω_m$ is slightly smaller than its actual value. On the other hand, one may obtain some valuable information on the properties of the underlying non-linear density field from the measure of weak lensing distortions.

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arXiv2000

Scaling laws in gravitational clustering for counts-in-cells and mass functions

We present in this article an analysis of some of the properties of the density field realized in numerical simulations for power-law initial power-spectra in the case of a critical density universe. We compare our numerical results in the non-linear regime with the predictions of a specific scaling model, focusing on its much wider range of applicability, which is one of its main advantages over the standard Press-Schechter approximation. We first check that the two-point correlation functions agree with the stable-clustering ansatz. Next we show that the statistics of the counts-in-cells obey the scaling law predicted by our scaling model. Then, we turn to mass functions of overdense and underdense regions. We first consider the mass function of "just collapsed" objects defined by a density threshold $Δ~177$. We note that the usual Press-Schechter prescription agrees reasonably well with the simulations (although there are some discrepancies) while the numerical results are also consistent with the scaling model. Then, we consider more general mass functions defined by different density thresholds which can even be negative. This is out of reach of the Press-Schechter approach while our scaling model can handle these mass functions and it shows a reasonably good agreement with numerical results. Finally, we consider objects defined by a constant radius condition. Thus, we find that the scaling model allows one to study many different classes of objects and it clarifies the links between various statistical tools.

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arXiv1999

The entropy history of the universe

Using a unified analytic model for quasars, galaxies, Lyman-alpha absorbers and the IGM, we obtain the redshift evolution of the temperature and the entropy of the gas and the corresponding cluster temperature - X-ray luminosity relation. We show that although quasars can easily reheat the IGM and raise its entropy up to the level required by current cluster observations the energy provided by supernovae is unlikely to be sufficient. Indeed, the efficiency factor needed for the supernova scenario is of order unity while for quasars we get a value ~ 0.008. Thus the IGM is more likely to have been reheated by quasars. Moreover, we find that if both scenarios are normalized to present observations the reheating due to quasars occurs somewhat earlier (z ~ 2) than for supernovae (z ~ 0.4) because of the sharp drop at low z of the quasar luminosity function. We also show that the Compton parameter y induced by the IGM is well below the observed upper limit in all cases. Finally, we note that such a reheating process may partly account for the decline at low redshift of the comoving star formation rate and of the quasar luminosity function. In particular, we show that the contradictory requirements arising from clusters and galaxies lead to a reheating temperature $T \sim 5 10^5$ K. On the other hand, the reionization process of the universe is almost not modified by these entropy sources.

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arXiv1999

Non-linear gravitational clustering: smooth halos, substructures and scaling exponents

Within the framework of hierarchical clustering scenarios, we investigate the consequences for the properties of virialized halos of the constraints provided by numerical simulations on the first few correlation functions. Thus, we show that the density field cannot be described by a collection of smooth halos with a universal density profile. This implies that substructures within larger objects play an important role (but a mean spherically averaged density profile may exist). In particular, a possible interpretation is that collapsed objects can be divided into an infinite hierarchy of smaller objects with increasingly large densities (these substructures might also be continuously destroyed and created by the long-range action of gravity). Finally, we present multifractal models (restricted to non-linear scales) which can describe in a natural way such non-linear density fields with increasingly large fluctuations at smaller scales. We relate their properties to the correlation functions and present a few constraints they are expected to satisfy, using theoretical considerations as well as constraints from numerical simulations. Thus, the simplest realistic model is the bifractal model described in Balian & Schaeffer (1989a). Moreover, we show that it should provide (at least) a very good approximation of the multifractal properties of the actual non-linear density field, hence of the probability distribution of the density contrast. The implications of this model (e.g. for galaxies) are detailed in other studies.

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arXiv1999

The reheating and reionization history of the universe

We incorporate quasars into an analytic model to describe the reheating and reionization of the universe. In combination with a previous study of galaxies and Lyman-$α$ clouds, we are able to provide a unified description of structure formation, verified against a large variety of observations. We also take into account the clumping of the baryonic gas in addition to the presence of collapsed objects. We consider two cosmologies: a critical universe with a CDM power-spectrum and an open universe with $Ω_0=0.3$, $Λ=0$. The derived quasar luminosity function agrees reasonably well with observations at $z<4.5$ and with constraints over larger redshifts from the HDF. The radiation produced by these objects at $z \sim 16$ slowly reheats the universe which gets suddenly reionized at $z_{ri}=6.8$ for the open universe ($z_{ri}=5.6$ for the critical density universe). The UV background radiation simultaneously increases sharply to reach a maximum of $J_{21} = 0.18$ at $z=2.6$, but shows strong ionization edges until $z \leq 1$. The metallicity of the gas increases quickly at high $z$ and is already larger than $0.01 Z_{\odot}$ at $z=10$. The QSO number counts and the helium opacity constrain the reionization redshift to be $z_{ri} \sim 6$. We confirm that a population of faint quasars is needed in order to satisfy the observations. Due to the low reionization redshift, the damping of CMB fluctuations is quite small, but future observations (e.g. with the NGST) of the multiplicity functions of radiation sources and of the HI and HeII opacities will strongly constrain scenarios in which reionization is due to QSOs.

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arXiv1999

The redshift evolution of Lyman-$α$ absorbers

We present a model for the Lyman-alpha absorbers that treats all objects (from the low-density forest clouds to the dense damped systems) in a unified description. This approach is consistent with an earlier model of galaxies (luminosity function, metallicity) but also with the known description of the density field in the small-scale non-linear regime. We consider two cosmological models: a critical universe $Ω=1$ with a CDM power-spectrum, and an open CDM universe with $Ω_0=0.3$, $Λ=0$. We reproduce the available data on column density distribution as a function of redshift, the value of the main new parameter, the background ionizing UV flux, being consistent with the observed limits. This allows a quantitatively trustable analytical description of the opacity, mass, size, velocity dispersion and metallicity of these absorbers, over a range of column densities spanning 10 orders of magnitude. Moreover, together with an earlier model of galaxy formation this draws a unified picture of the redshift evolution of structures in the universe, from underdense clouds to massive high density galaxies, from weak to very deep potential wells.

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arXiv1998

Structure formation: a spherical model for the evolution of the density distribution

Within the framework of hierarchical clustering we show that a simple Press-Schechter-like approximation, based on spherical dynamics, provides a good estimate of the evolution of the density field in the quasi-linear regime up to $Σ\sim 1$. Moreover, it allows one to recover the exact series of the cumulants of the probability distribution of the density contrast in the limit $Σ\to 0$ which sheds some light on the rigorous result and on ``filtering''. We also obtain similar results for the divergence of the velocity field. Next, we extend this prescription to the highly non-linear regime, using a stable-clustering approximation. Then we recover a specific scaling of the counts-in-cells which is indeed seen in numerical simulations, over a well-defined range. To this order we also introduce an explicit treatment of the behaviour of underdensities, which takes care of the normalization and is linked to the low-density bubbles and the walls one can see in numerical simulations. We compare this to a 1-dimensional adhesion model, and we present the consequences of our prescription for the power-law tail and the cutoff of the density distribution.

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