arXiv subjects

Sergei F. Shandarin

Publications and source records attributed to Sergei F. Shandarin.

At least 37 records · Page 2Linked to original sources

arXiv2002

Effects of Noise on Galaxy Isophotes

The study of shapes of the images of objects is an important issue not only because it reveals its dynamical state but also it helps to understand the object's evolutionary history. We discuss a new technique in cosmological image analysis which is based on a set of non-parametric shape descriptors known as the Minkowski Functionals (MFs). These functionals are extremely versatile and under some conditions give a complete description of the geometrical properties of objects. We believe that MFs could be a useful tool to extract information about the shapes of galaxies, clusters of galaxies and superclusters. The information revealed by MFs can be utilized along with the knowledge obtained from currently popular methods and thus could improve our understanding of the true shapes of cosmological objects.

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arXiv2002

Morphology of the Secondary CMB Anisotropies: the Key to "Smoldering" Reionization

We show how the morphological analysis of the maps of the secondary CMB anisotropies can detect an extended period of ``smoldering'' reionization, during which the universe remains partially ionized. Neither radio observations of the redshifted 21cm line nor IR observations of the redshifted Lyman-alpha forest will be able to detect such a period. The most sensitive to this kind of non-gaussianity parameters are the number of regions in the excursion set, the perimeter of the excursion set, and the genus of the largest (by area) region. For example, if the universe reionized fully at z=6, but maintained about 1/3 mean ionized fraction since z=20, then a 2 arcmin map with 500x500 pixel resolution and a signal-to-noise ratio S/N=1/2 allows to detect the non-gaussianity due to reionization with better than 99% confidence level.

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arXiv2002

Morphological Measures of nonGaussianity in CMB Maps

We discuss the tests of nonGaussianity in CMB maps using morphological statistics known as Minkowski functionals. As an example we test degree-scale cosmic microwave background (CMB) anisotropy for Gaussianity by studying the \qmask map that was obtained from combining the QMAP and Saskatoon data. We compute seven morphological functions $M_i(\dt)$, $i=1,...,7$: six \mf and the number of regions $N_c$ at a hundred $\dt$ levels. We also introduce a new parameterization of the morphological functions $M_i(A)$ in terms of the total area $A$ of the excursion set. We show that the latter considerably decorrelates the morphological statistics and makes them more robust because they are less sensitive to the measurements at extreme levels. We compare these results with those from 1000 Gaussian Monte Carlo maps with the same sky coverage, noise properties and power spectrum, and conclude that the \qmask map is neither a very typical nor a very exceptional realization of a Gaussian field. At least about 20% of the 1000 Gaussian Monte Carlo maps differ more than the \qmask map from the mean morphological parameters of the Gaussian fields.

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arXiv2002

Testing non-Gaussianity in CMB Maps by Morphological Statistic

The assumption of Gaussianity of the primordial perturbations plays an important role in modern cosmology. The most direct test of this hypothesis consists in testing Gaussianity of the CMB maps. Counting the pixels with the temperatures in given ranges and thus estimating the one point probability function of the field is the simplest of all the tests. Other usually more complex tests of Gaussianity generally use a great deal of the information already contained in the probability function. However, the most interesting outcome of such a test would be the signal of non-Gaussianity independent of the probability function. It is shown that the independent information has purely morphological character i.e. it depends on the geometry and topology of the level contours only. As an example we discuss in detail the quadratic model $v=u+α(u^2-1)$ ($u$ is a Gaussian field with $\bar{u}=0$ and $ =1$, $α$ is a parameter) which may arise in slow-roll or two-field inflation models. We show that in the limit of small amplitude $α$ the full information about the non-Gaussianity is contained in the probability function. If other tests are performed on this model they simply recycle the same information. A simple procedure allowing to assess the sensitivity of any statistics to the morphological information is suggested. We provide an analytic estimate of the statistical limit for detecting the quadratic non-Gaussianity $\a_c$ as a function of the map size in the ideal situation when the scale of the field is resolved. This estimate is in a good agreement with the results of the Monte Carlo simulations of $256^2$ and $1024^2$ maps. The effect of resolution on the detection quadratic non-Gaussianity is also briefly discussed.

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arXiv2001

Constraining Cosmological Models by the Cluster Mass Function

We present a comparison between two observational and three theoretical mass functions for eight cosmological models suggested by the data from the recently completed BOOMERANG-98 and MAXIMA-1 cosmic microwave background (CMB) anisotropy experiments as well as peculiar velocities (PVs) and type Ia supernovae (SN) observations. The cosmological models have been proposed as the best fit models by several groups. We show that no model is in agreement with the abundances of X-ray clusters at $\sim 10^{14.7} h^{-1}M_{\odot}$.On the other hand, we find that the BOOM+MAX+{\sl COBE}:I, Refined Concordance and $Λ$MDM are in a good agreement with the abundances of optical clusters. The P11 and especially Concordance models predict a slightly lower abundances than observed at $\sim 10^{14.6} h^{-1}M_{\odot}$. The BOOM+MAX+{\sl COBE}:II and PV+CMB+SN models predict a slightly higher abundances than observed at $\sim 10^{14.9} h^{-1}M_{\odot}$. The nonflat MAXIMA-1 is in a fatal conflict with the observational cluster abundances and can be safely ruled out.

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arXiv2000

The Cosmological Mass Function in the Zel'dovich Approximation

The Press-Schechter theory of the cosmological mass function and its modifications allow to constraint cosmological scenarios of the structure formation. Recently a few new models have been suggested that explored the influence of anisotropic collapse on the shape of the mass function. I discuss in more detail a particular model that assumes that a fluid particle becomes a part of a gravitationally bound halo when the smallest eigenvalue of the deformation tensor of the filtered initial density field reaches a certain threshold (like the filtered density contrast reaches the threshold in the Press-Schechter formalism). Choosing the smallest eigenvalue guarantees that the fluid particle in question experiences collapse along all three axes. The model shows a better agreement with the N-body simulations than the standard Press-Schechter model.

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arXiv1999

Evidence for Filamentarity in the Las Campanas Redshift Survey

We apply Shapefinders, statistical measures of `shape' constructed from two dimensional partial Minkowski functionals, to study the degree of filamentarity in the Las Campanas Redshift Survey (LCRS). In two dimensions, three Minkowski functionals characterise the morphology of an object, they are: its perimeter (L), area (S), and genus. Out of L and S a single dimensionless Shapefinder Statistic, F can be constructed (0 <=F <=1). F acquires extreme values on a circle (F = 0) and a filament (F = 1). Using F, we quantify the extent of filamentarity in the LCRS by comparing our results with a Poisson distribution with similar geometrical properties and having the same selection function as the survey. Our results unambiguously demonstrate that the LCRS displays a high degree of filamentarity both in the Northern and Southern galactic sections a result that is in general agreement with the visual appearance of the catalogue. It is well known that gravitational clustering from Gaussian initial conditions gives rise to the development of non-Gaussianity reflected in the formation of a network-like filamentary structure on supercluster scales. Consequently the fact that the smoothed LCRS catalogue shows properties consistent with those of a Gaussian random field (Colley 1997) whereas the unsmoothed catalogue demonstrates the presence of filamentarity lends strong support to the conjecture that the large scale clustering of galaxies is driven by gravitational instability.

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arXiv1999

Disentangling the Cosmic Web I: Morphology of Isodensity Contours

We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to test global properties of the density field. Furthermore, we identify coherent objects at various threshold levels and calculate their partial Minkowski functionals. We propose a set of two derived dimensionless quantities, planarity and filamentarity, which reduce the morphological information in a simple and intuitive way. Several simulations of the gravitational evolution of initial power-law spectra provide a framework for systematic tests of our method.

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arXiv1999

Minkowski Functionals and Cluster Analysis for CMB Maps

We suggest novel statistics for the CMB maps that are sensitive to non-Gaussian features. These statistics are natural generalizations of the geometrical and topological methods that have been already used in cosmology such as the cumulative distribution function and genus. We compute the distribution functions of the Partial Minkowski Functionals for the excursion set above or bellow a constant temperature threshold. Minkowski Functionals are additive and are translationally and rotationally invariant. Thus, they can be used for patchy and/or incomplete coverage. The technique is highly efficient computationally (it requires only O(N) operations, where N is the number of pixels per one threshold level). Further, it allows to split large data sets into smaller subsets. The full advantage of these statistics can be obtained only on very large data sets. We apply it to the 4-year DMR COBE data corrected for the Galaxy contamination as an illustration of the technique.

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arXiv1999

Comparison of Analytical Mass Functions with Numerical Simulations

We present numerical testing results of our mass function derived in our previous paper, and compare the testing results with those of the popular Press-Schechter (PS) mass function. Two fiducial models are considered for the test: the scale-free power-law spectra P(k) \propto k^{n} with spectral indices n=-1, 0 and the standard cold dark matter (SCDM) model with Omega =1 and h=0.5. For the power-law models, we use numerical data averaged over several different output times: ten output times from two N-body realizations for the n=-1 power-law model; four outputs from one realization for the n=0 model. While for the SCDM model, we consider four outputs separately at redshifts z = 0, 0.43, 1.14 and 1.86 from one large N-body simulations. The comparison results show that our mass function fits the numerical data in a much improved way over the PS one. Thus, we expect that our mass function can be a viable alternative of the PS mass function in applications to various areas.

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arXiv1999

Multiple-streaming and the Probability Distribution of Density in Redshift Space

We examine several aspects of redshift distortions by expressing the redshift-space density in terms of the eigenvalues and orientation of the local Lagrangian deformation tensor. We explore the importance of multiple-streaming using the Zel'dovich approximation (ZA), and compute the average number of streams in real and redshift-space. It is found that multiple-streaming can be significant in redshift-space but negligible in real-space, even at moderate values of the linear fluctuation amplitude ($σ< 1$). Moreover, unlike their real-space counter-parts, redshift-space multiple-streams can flow past each other with minimal interactions. Such nonlinear redshift-space effects, which operate even when the real-space density field is quite linear, could suppress the classic compression of redshift-structures predicted by linear theory (Kaiser 1987). We also compute using the ZA the probability distribution function (PDF) of density, as well as $S_3$, in real and redshift-space, and compare it with the PDF measured from N-body simulations. The role of caustics in defining the character of the high density tail is examined. It is found that (non-Lagrangian) smoothing, due to both finite resolution or discreteness and small-scale velocity dispersions, is very effective in erasing caustic structures, unless the initial power spectrum is sufficiently truncated.

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arXiv1998

The Large Scale Biasing and the Primordial Gravitational Potential

We modified the Press-Schechter (PS) formalism and then analytically derived a constrained mass distribution function n(M|varphi) for the regions having some specified value of the primordial gravitational potential, varphi. The resulting modified PS theory predicts that gravitationally bound clumps with masses corresponding to rich clusters are significantly biased toward the regions of negative primordial potential - the troughs of the potential. The prediction is quantitative, depending on the mass and the depth of the troughs, which can be tested in large N-body simulations. As an illustration of the magnitude of the effect we calculate the constrained mass function for the CDM model with Gamma = Omega h = 0.25 normalized to sigma_{8} = 1. In particular, we show that the probability of finding a clump of mass 10^{14} - 10^{15}h^{-1}M_{odot} in the region of negative initial potential is 1.3 - 3 times greater (depending on the mass) than that in the region of positiveinitial potential. The scale of the potential fluctuations R_{varphi}=sqrt{3} sigma_{varphi}/sigma_{varphi'} is shown to be approx 120 h^{-1} Mpc for the spectrum in question. The rms mass density contrast on this scale is only about sigma_{delta}(R_{varphi}) approx 0.03. Assuming that the modified PS theory is statistically correct, we conclude that clusters are significantly biased (b ge 10, b is a bias factor defined by Delta n_{cl}/ n_{cl} = b Delta rho_m/rho_m) toward the regions having negative initial potential.

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arXiv1998

Morphology of Clusters and Superclusters in N-body simulations of Cosmological Gravitational Clustering

We analyse shapes of overdense regions (clusters and superclusters) in controlled N-body simulations of gravitational clustering with power law initial spectra P(k) \propto k^n, n = -3, -2, -1, 0. At values of the density just above the percolation transition the number of distinct (isolated) clusters peaks and we use this `natural threshold' to study the shapes and multiplicity function of clusters and superclusters. We find that the extent of both filamentarity and pancakeness increases as the simulation evolves, the former being appreciably larger than the latter at virtually all epochs and for all spectra considered by us. Our results also show that high density regions within very massive clusters/superclusters are likely to be noticeably filamentary or pancake/ribbon-like when compared to the less dense regions within these objects. We make a detailed study of two, moment-based `shape statistics' proposed, respectively, by Babul & Starkman (BS) and Luo & Vishniac (LV) and find that both LV and BS have certain built-in limitations: LV is biased towards oblate structures and tends to overemphasise this property; neither BS nor LV correctly describe the shape of strongly curved or topologically nontrivial objects. For instance, a thin filamentary torus and a ribbon are both described by BS and LV as being pancakes ! By contrast Shapefinders, a new shape diagnostic not constructed from density moments but from Minskowski functionals, does not suffer from these limitations and appears to faithfully reproduce the shapes of both simple and topologically complex objects.

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arXiv1998

Filaments and Pancakes in the IRAS 1.2 Jy Redshift Catalogue

We explore shapes of clusters and superclusters in the IRAS 1.2 Jy redshift survey with three reconstructions spanning the range β= 0.1, 0.5, 1.0, where β= Ω^{0.6}/b, b is the bias factor and Ωthe present value of the dimensionless matter density. Comparing our results to Gaussian randomized reconstructions of the IRAS catalogue, we find structures having both planar and filamentary properties. For β= 0.5, 1.0 the largest structures in the survey have a distinct tendency to be filament-like} in general agreement with the results of N-body simulations.

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arXiv1998

Shapefinders: A new shape diagnostic for large scale structure

We construct a set of shape-finders which determine shapes of compact surfaces (iso-density surfaces in galaxy surveys or N-body simulations) without fitting them to ellipsoidal configurations as done earlier. The new indicators arise from simple, geometrical considerations and are derived from fundamental properties of a surface such as its volume, surface area, integrated mean curvature and connectivity characterized by the Genus. These `Shapefinders' could be used to diagnose the presence of filaments, pancakes and ribbons in large scale structure. Their lower-dimensional generalization may be useful for the study of two-dimensional distributions such as temperature maps of the Cosmic Microwave Background.

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arXiv1997

The Cosmological Mass Distribution Function in the Zel'dovich Approximation

An analytic approximation to the mass function for gravitationally bound objects is presented. We base on the Zel'dovich approximation to extend the Press-Schechter formalism to a nonspherical dynamical model. A simple extrapolation of that approximation suggests that the gravitational collapse along all three directions which eventually leads to the formation of real virialized objects - clumps occur in the regions where the lowest eigenvalue of the deformation tensor,lambda_{3}, is positive. We derive the conditional probability of lambda_{3}>0 as a function of the linearly extrapolated density contrast, delta, and the conditional probability distribution of delta provided that lambda_{3}>0. These two conditional probability distributions show that the most probable density of the bound regions (lambda_{3}>0) is roughly 1.5 at the characteristic mass scale, and that the probability of lambda_{3}>0 is almost unity in the highly overdense regions (delta>3*sigma). Finally an analytic mass function of clumps is derived with a help of one simple ansatz which is employed to treat the multistream regions beyond the validity of the Zel'dovich approximation. The resulting mass function is renormalized by a factor of 12.5, which we justify with a sharp k-space filter by means of the modified Jedamzik analysis. Our mass function is shown to be different from the Press-Schechter one, having a lower peak and predicting more small-mass objects.

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arXiv1997

Dark Matter, Discreteness and Collision Error in Cosmological N-Body Simulations

We report on a series of tests of agreement between three types of N-body simulations: PM, P$^3$M, and Tree codes. We find good agreement in both the individual and the statistical properties only on scales larger than the mean interparticle separation. As a result, we question most numerical results at and below below galaxy scales, either concerning primordial dark matter or baryonic matter coupled to it by gravitation. Mass resolution (specifically, sufficient to have the mean interparticle separation comparable to the smoothing scales) appears be necessary for results to converge.

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arXiv1997

Fundamental Discreteness Limitations of Cosmological N-Body Clustering Simulations

We explore some of the effects that discreteness and two-body scattering may have on N-body simulations with ``realistic'' cosmological initial conditions. We use an identical subset of particles from the initial conditions for a $128^3$ Particle-Mesh (PM) calculation as the initial conditions for a variety P$^3$M and Tree code runs. We investigate the effect of mass resolution (the mean interparticle separation) since most ``high resolution'' codes only have high resolution in gravitational force. The phase-insensitive two--point statistics, such as the power spectrum (autocorrelation) are somewhat affected by these variations, but phase-sensitive statistics show greater differences. Results converge at the mean interparticle separation scale of the lowest mass-resolution code. As more particles are added, but the force resolution is held constant, the P$^3$M and the Tree runs agree more and more strongly with each other and with the PM run which had the same initial conditions. This shows high particle density is necessary for correct time evolution, since many different results cannot all be correct. However, they do not so converge to a PM run which continued the fluctuations to small scales. Our results show that ignoring them is a major source of error on comoving scales of the missing wavelengths. This can be resolved by putting in a high particle density. Since the codes never agree well on scales below the mean comoving interparticle separation, we find little justification for quantitative predictions on this scale. Some measures vary by 50%, but others can be off by a factor of three or more. Our results suggest possible problems with the density of galaxy halos, formation of early generation objects such as QSO absorber clouds, etc.

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