arXiv subjects

Dipak Munshi

Publications and source records attributed to Dipak Munshi.

68 records · Page 4Linked to original sources

arXiv2000

Cosmic Statistics through Weak Lenses

Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical {\em ansatz}, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small angular scales (i.e. at high resolution), where the usual perturbative calculations of matter clustering no longer apply. We build on these studies in order to develop a complete picture of weak lensing at small smoothing angles. In particular, we study the full probability distribution function, bias and other multipoint statistics for the ``hot spots'' of the convergence field induced by weak lensing, and relate these to the statistics of overdense regions in underlying mass distribution. It is already known that weak lensing can constrain the background geometry of the Universe, but we further show that it can also provide valuable information about the statistics of collapsed objects and the physics of collisionless clustering. Our results are particularly important for future observations which will, at least initially, focus on small smoothing angles.

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arXiv2000

Probing The Gravity Induced Bias with Weak Lensing: Test of Analytical results Against Simulations

Future weak lensing surveys will directly probe the density fluctuation in the universe. Recent studies have shown how the statistics of the weak lensing convergence field is related to the statistics of collapsed objects. Extending earlier analytical results on the probability distribution function of the convergence field we show that the bias associated with the convergence field can directly be related to the bias associated with the statistics of underlying over-dense objects. This will provide us a direct method to study the gravity induced bias in galaxy clustering. Based on our analytical results which use the hierarchical {\em ansatz} for non-linear clustering, we study how such a bias depends on the smoothing angle and the source red-shift. We compare our analytical results against ray tracing experiments through N-body simulations of four different realistic cosmological scenarios and found a very good match. Our study shows that the bias in the convergence map strongly depends on the background geometry and hence can help us in distinguishing different cosmological models in addition to improving our understanding of the gravity induced bias in galaxy clustering.

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arXiv1999

Statistics of Weak Lensing at Small Angular Scales: Analytical Predictions for Lower Order Moments

Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasilinear scales as they relied on perturbative calculations. On the other hand, observational surveys are likely to probe angular scales less than 10 arcminutes, for which the relevant physical length scales are in the nonlinear regime of gravitational clustering. We use the hierarchical ansatz to compute the multi-point statistics of the weak lensing convergence for these small smoothing angles. We predict the multi-point cumulants and cumulant correlators up to fourth order and compare our results with high resolution ray tracing simulations. Averaging over a large number of simulation realizations for four different cosmological models, we find close agreement with the analytical calculations. In combination with our work on the probability distribution function, these results provide accurate analytical models for the full range of weak lensing statistics. The models allow for a detailed exploration of cosmological parameter space and of the dependence on angular scale and the redshift distribution of source galaxies. We compute the dependence of the higher moments of the convergence on the parameters Omega and Lambda and on the nature of gravitational clustering.

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arXiv1999

The Statistics of Weak Lensing at Small Angular Scales: Probability Distribution Function

Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by modeling the statistics of the underlying density field in the highly nonlinear regime. We propose a new method to model the complete probability distribution function of the convergence field as a function of smoothing angle and source redshift. The model relies on a hierarchical ansatz for the behavior of higher order correlations of the density field. We compare our results with ray tracing simulations and find very good agreement over a range of smoothing angles. Whereas the density probability distribution function is not sensitive to the cosmological model, the probability distribution function for the convergence can be used to constrain both the power spectrum and cosmological parameters.

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arXiv1999

Weak Lensing from Strong Clustering

We investigate the effect of weak gravitational lensing in the limit of small angular scales where projected galaxy clustering is strongly nonlinear. This is the regime likely to be probed by future weak lensing surveys. We use well-motivated hierarchical scaling arguments and the plane-parallel approximation to study multi-point statistical properties of the convergence field. These statistics can be used to compute the vertex amplitudes in tree models of hierarchical clustering; these can be compared with similar measurements from galaxy surveys, leading to a powerful probe of galaxy bias.

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arXiv1999

Bias and Hierarchical Clustering

It is now well established that galaxies are biased tracers of the distribution of matter, although it is still not known what form this bias takes. In local bias models the propensity for a galaxy to form at a point depends only on the overall density of matter at that point. Hierarchical scaling arguments allow one to build a fully-specified model of the underlying distribution of matter and to explore the effects of local bias in the regime of strong clustering. Using a generating-function method developed by Bernardeau & Schaeffer (1992), we show that hierarchical models lead one directly to the conclusion that a local bias does not alter the shape of the galaxy correlation function relative to the matter correlation function on large scales. This provides an elegant extension of a result first obtained by Coles (1993) for Gaussian underlying fields and confirms the conclusions of Scherrer & Weinberg (1998) obtained using a different approach. We also argue that particularly dense regions in a hierarchical density field display a form of bias that is different from that obtained by selecting such peaks in Gaussian fields: they are themselves hierarchically distributed with scaling parameters $S_p=p^{(p-2)}$. This kind of bias is also factorizable, thus in principle furnishing a simple test of this class of models.

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arXiv1999

From Snakes to Stars, the Statistics of Collapsed Objects - II. Testing a Generic Scaling Ansatz for Hierarchical Clustering

We develop a diagrammatic technique to represent the multi-point cumulative probability density function (CPDF) of mass fluctuations in terms of the statistical properties of individual collapsed objects and relate this to other statistical descriptors such as cumulants, cumulant correlators and factorial moments. We use this approach to establish key scaling relations describing various measurable statistical quantities if clustering follows a simple general scaling ansatz, as expected in hierarchical models. We test these detailed predictions against high-resolution numerical simulations. We show that, when appropriate variables are used, the count probability distribution function (CPDF) and void probability distribution function (VPF) shows clear scaling properties in the non-linear regime. Generalising the results to the two-point count probability distribution function (2CPDF), and the bivariate void probability function (2VPF) we find good match with numerical simulations. We explore the behaviour of the bias associated with collapsed objects in limit of large separations, finding that it depends only on the intrinsic scaling parameter associated with collapsed objects and that the bias for two different objects can be expressed as a product of the individual biases of the objects. Finally we use hierarchal ansatz to develop a novel technique for correcting finite-volume effects in the estimation of multi-point statistical quantities from observational data (abridged).

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arXiv1998

From Snakes to Stars, the Statistics of Collapsed Objects - I. Lower--order Clustering Properties

The highly nonlinear regime of gravitational clustering is characterized by the presence of scale-invariant form of many-body correlation functions. Useful insights can be obtained by investigating the consequences of a generic scaling {\em ansatz}. Extending earlier studies by Bernardeau & Schaeffer (1992) we calculate the detailed consequences of such scaling. We generalise the two-point cumulant correlators to a hierarchy of multi-point cumulant correlators (MCC). We introduce the concept of reduced cumulant correlators (RCC) and their related generating functions. Using analytical and diagrammatic method we show that every new vertex of the tree representation of higher-order correlations has its own reduced cumulant correlator. In the limit of large separations, MCCs of arbitrary order can be expressed in terms of RCCs of the same and lower order. We relate the generating functions of RCCs with the statistics of {\em collapsed} objects. We develop the hierarchy for the correlation functions of overdense regions. In this vein, we compute the lower-order cumulants and cumulant correlators for overdense regions. Our study shows how they vary as a function of the initial power spectrum of primordial density fluctuations (abridged).

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arXiv1998

Generalised Cumulant Correlators and Hierarchical Clustering

The cumulant correlators, $C_{pq}$, are statistical quantities that generalise the better-known $S_p$ parameters; the former are obtained from the two-point probability distribution function of the density fluctuations while the latter describe only the one-point distribution. If galaxy clustering develops from Gaussian initial fluctuations and a small-angle approximation is adopted, standard perturbative methods suggest a particular hierarchical relationship of the $C_{pq}$ for projected clustering data, such as the APM survey. We establish the usefulness of the two-point cumulants for describing hierarchical clustering by comparing such calculations against available measurements from projected catalogs, finding very good agreement. We extend the idea of cumulant correlators to multi-point {\em generalised} cumulant correlators (related to the higher-order correlation functions). We extend previous studies in the highly nonlinear regime to express the generalised cumulant correlators in terms of the underlying ``tree amplitudes'' of hierarchical scaling models. Such considerations lead to a technique for determining these hierarchical amplitudes, to arbitrary order, from galaxy catalogs and numerical simulations. Knowledge of these amplitudes yields important clues about the phenomenology of gravitational clustering. For instance, we show that three-point cumulant correlator can be used to separate the tree amplitudes up to sixth order. We also combine the particular hierarchical {\em ansatz} of Bernardeau & Schaeffer (1992) with extended and hyperextended perturbation theory to infer values of the tree amplitudes in the highly nonlinear regime.

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arXiv1998

Cumulant Correlators in 2D and 3D Scale Free Simulations

Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions and related moments. Methods based on factorial moments of two point count probability distribution (cumulant correlators) were recently shown to be efficient in subtracting discreteness effects and extracting useful information from galaxy catalogs. We use these cumulant correlators $Q_{NM}$ to study clustering in scale free simulations both in two and three dimensions. Using this method in the highly nonlinear regime we were able to separate hierarchal amplitudes $Q_3, R_a and R_b$ associated with different tree graphs contributing to third and fourth order correlation functions. They were found to increase with power on large scales. Results based on factorial moments of one point cumulants show very good agreement with that on cumulant correlators. Comparison of simulation results with perturbation theory and extended perturbation theory were found to be in reasonable agreement. Comparisons were also made against predictions from hierarchal models for higher order correlations. We argue that finite volume corrections are very important for computation of cumulant correlators.

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arXiv1997

Skewness in the Cosmic Microwave Background Anisotropy from Inflationary Gravity Wave Background

In the context of inflationary scenarios, the observed large angle anisotropy of the Cosmic Microwave Background (CMB) temperature is believed to probe the primordial metric perturbations from inflation. Although the perturbations from inflation are expected to be gaussian random fields, there remains the possibility that nonlinear processes at later epochs induce ``secondary'' non-gaussian features in the corresponding CMB anisotropy maps. The non-gaussianity induced by nonlinear gravitational instability of scalar (density) perturbations has been investigated in existing literature. In this paper, we highlight another source of non-gaussianity arising out of higher order scattering of CMB photons off the metric perturbations. We provide a simple and elegant formalism for deriving the CMB temperature fluctuations arising due to the Sachs-Wolfe effect beyond the linear order. In particular, we derive the expression for the second order CMB temperature fluctuations. The multiple scattering effect pointed out in this paper leads to the possibility that tensor metric perturbation, i.e., gravity waves (GW) which do not exhibit gravitational instability can still contribute to the skewness in the CMB anisotropy maps. We find that in a flat $Ω=1$ universe, the skewness in CMB contributed by gravity waves via multiple scattering effect is comparable to that from the gravitational instability of scalar perturbations for equal contribution of the gravity waves and scalar perturbations to the total rms CMB anisotropy. The secondary skewness is found to be smaller than the cosmic variance leading to the conclusion that inflationary scenarios do predict that the observed CMB anisotropy should be statistically consistent with a gaussian random distribution.

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arXiv1997

Modelling the evolution of correlation functions in gravitational clustering

Padmanabhan (1996) has suggested a model to relate the nonlinear two - point correlation function to the linear two - point correlation function. In this paper, we extend this model in two directions: (1) By averaging over the initial Gaussian distribution of density contrasts, we estimate the spectral dependence of the scaling between nonlinear and linear correlation functions. (2) By using a physically motivated ansatz, we generalise the model to N-point correlation functions and relate the nonlinear, volume averaged, N-point correlation function $\barξ_N(x,a)$ with linearly extrapolated volume averaged 2-point correlation function $\bar ξ_2(l,a)$ evaluated at a different scale. We compare the point of transition between different regimes obtained from our model with numerical simulations and show that the spectral dependence of the scaling relations seen in the simulations can be easily understood. Comparison of the calculated form of $\barξ_N$ with the simulations show reasonable agreement. We discuss several implications of the results.

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arXiv1995

Skewness of Cosmic Microwave Background Temperature Fluctuations Due to Non-linear Gravitational Instability

Skewness of temperature fluctuations of the cosmic microwave background (CMB) produced by initially Gaussian adiabatic perturbations with the flat (Harrison-Zeldovich) spectrum, which arises due to non-linear corrections to a gravitational potential at the matter-dominated stage, is calculated quantitatively. For the standard CDM model, the effect appears to be smaller than expected previously and lies below the cosmic variance limit even for small angles. The sign of the skewness is opposite to that of the skewness of density perturbations.

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arXiv1994

Non-Linear Approximations to Gravitational Instability: A Comparison in the Quasi-Linear Regime

We compare different nonlinear approximations to gravitational clustering in the weakly nonlinear regime, using as a comparative statistic the evolution of non-Gaussianity which can be characterised by a set of numbers $S_p$ describing connected moments of the density field at the lowest order in $<δ^2>$: $<δ^n>_c \simeq S_n<δ^2>^{n-1}$. Generalizing earlier work by Bernardeau (1992) we develop an ansatz to evaluate all $S_p$ in a given approximation by means of a generating function which can be shown to satisfy the equations of motion of a homogeneous spherical density enhancement in that approximation. On the basis of the values of we show that approximations formulated in Lagrangian space (such as the Zeldovich approximation and its extensions) are considerably more accurate than those formulated in Eulerian space such as the Frozen Flow and Linear Potential approximations. In particular we find that the $n$th order Lagrangian perturbation approximation correctly reproduces the first $n+1$ parameters $S_n$. We also evaluate the density probability distribution function for the different approximations in the quasi-linear regime and compare our results with an exact analytic treatment in the case of the Zeldovich approximation.

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