Research Papers (TP)
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Item Zeldovich approximation and the probability distribution for the smoothed density field in the nonlinear regime(American Astronomical Society, 1993-06-20) Padmanabhan, T.; Subramanian, KandaswamyThe study of large-scale structure in the Universe is often based on the observed density distribution of matter smoothed by a suitable filter function. The probability distribution for this smoothed density field in the nonlinear regime is studied using the Zel'dovich approximation. When the shear term of the velocity field is not too large, one can obtain a reasonably good analytic approximation tho this probability distribution. The properties of this distribution are discussed and compared with other attempts along similar lines.Item Transfer of power in nonlinear gravitational clustering(Wiley-Blackwell, 1996-12-15) Bagla, J. S.; Padmanabhan, T.We investigate the transfer of power between different scales and the coupling of modes during the non-linear evolution of gravitational clustering in an expanding universe. We start with a power spectrum of density fluctuations that is exponentially damped outside a narrow range of scales, and use numerical simulations to study the evolution of this power spectrum. Non-linear effects generate power at other scales, with most power flowing from larger to smaller scales. The ‘cascade’ of power leads to equipartition of energy at smaller scales, implying a power spectrum with index n ~ - 1. We find that such a spectrum is produced in the range 1 < ð < 200 for density contrast ð. This result continues to hold even when small-scale power is added to the initial power spectrum. Semi-analytic models for gravitational clustering suggest a tendency for the effective index to move towards a critical index Nc ~-1. We find that such a spectrum is produced in the range 1< ð<200 for density contrast ð. This result continues to hold even when small-scale power is added to the initial power spectrum. Semi-analytic models for gravitational clustering suggest a tendency for the effective index to move towards a critical index Nc ~-1 in this range. For n< Nc , power in this range grows faster than linear rate, while if n> Nc , it grows at a slower rate- thereby changing the index closer to Nc. At scales larger than the narrow range of scales with initial power, a k⁴ tail is produced. We demonstrate that non-linear small scales do not affect the growth of perturbations at larger scales.Item Scaling properties of nonlinear gravitational clustering(Royal Astronomical Society, 1994-09-16) Nityananda, R.; Padmanabhan, T.Hamilton et al. recently proposed the idea that the growth of density perturbations in an expanding universe is govemed by a general scaling law, and showed agreement with existing numerical simulations. We examine the possible origin of this scaling behaviour in more detail. The underlying equations of motion are cast in a suggestive form, and motivate a conjecture that the scaled pair velocity, h(x, α)≡ -[v/(αx)], depends on the expansion factor α and comoving coordinate x only through the density contrast ξ-(x, α) (the two-point correlation averaged over a sphere of radius x). This leads naturally to the proposed scaling law - the true non-linear density contrast is a universal function of the density contrast ξ-L(l,a), computed in the linear theory and evaluated at a scale lwhich is derived to be l =x(1 +ξ-)¹/³. Apart from basing the proposed scaling form on an explicit dynamical hypothesis, this gives a convenient solution for the scaling function in terms of the input pair velocity. Possibilities for further elaboration of this approach in interpreting simulations of non-linear gravitational clustering are briefly discussed.Item Patterns in non-linear gravitational clustering: a numerical investigation(American Astronomical Society, 1996-02-15) Padmanabhan, T.; Cen, Renyue; Ostriker, Jeremiah P.; Summers, F. J.The nonlinear clustering of dark matter particles in an expanding universe is usually studied by N-body simulations. One can gain some insight into this complex problem if simple relations between physical quantities in the linear and nonlinear regimes can be extracted from the results of N-body simulations. Hamilton and coworkers and Nityananda & Padmanabhan have made an attempt in this direction by relating the mean relative pair velocities to the mean correlation function in a useful manner. We investigate this relation and other closely related issues in detail for six different power spectra: power laws with spectral indexes n = -2 and -1; cold dark matter (CDM) and hot dark matter models with density parameter Ω = t1 a CDM model including a cosmological constant (Α) with ΩCDM = 0.4 and ΩΑ = 0.6; and an n = -1 model with Ω = 0.1. We find the following: (t) Power-law spectra lead to self-similar evolution in an Ω = 1 universe. (2) Stable clustering does not hold in an Ω = 1 universe to the extent that our simulations can ascertain. (3) Stable clustering is a better approximation in the case of an Ω < 1 universe in which structure formation freezes out at some low redshift. (4) The relation between the dimensionless pair velocity and the mean correlation function, ξ, is only approximately independent of the shape of the power spectrum. At the nonlinear end, the asymptotic value of the dimensionless pair velocity decreases with increasing small-scale power because the stable clustering assumption is not universally true. (5) The relation between the evolved ξ and the linear regime ξ is also not universal but shows a weak spectrum dependence. We present simple theoretical arguments for these conclusions.Item Nonlinear gravitational clustering: Dreams of a paradigm(American Astronomical Society, 1997-09-08) Padmanabhan, T.; Engineer, SunuWe discuss the late-time evolution of the gravitational clustering in an expanding universe, based on the nonlinear scaling relations (NSR) that connect the nonlinear and linear two-point correlation functions. The existence of critical indices for the NSR suggests that the evolution may proceed toward a universal profle that does not change its shape at late times. We begin by clarifying the relation between the density profles of the individual halos and the slope of the correlation function, and we discuss the conditions under which the slopes of the correlation function at the extreme nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a profle that preserves the shape at late times, then the correlation function should grow as a2 (in a )\1 universe), even at nonlinear scales. We prove that such exact solutions do not exist ; however, there exists a class of solutions ("psuedolinear profles") that evolve as a2 to a good approximation. It turns out that pseudolinear profles are the correlation functions that arise if the individual halos are assumed to be isothermal spheres. They are also confgurations of mass in which the nonlinear effects of gravitational clustering are a minimum, and hence they can act as building blocks of the nonlinear universe. We discuss the implications of this result.Item Non-linear density evolution from an improved spherical collapse model(Wiley-Blackwell, 1999-11-30) Engineer, Sunu; Kanekar, Nissim; Padmanabhan, T.We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we introduce a physically motivated closure condition which specifies the dependence of the additional terms on the density contrast, δ. The modified equation can be used to model the behaviour of an overdense region over a sufficiently large range of δ. The key new idea is a Taylor series expansion in (1/δ) to model the non-linear epoch. We show that the modified equations quite generically lead to the formation of stable structures in which the gravitational collapse is halted at around the virial radius. The analysis also allows us to connect up the behaviour of individual overdense regions with the non-linear scaling relations satisfied by the two point correlation function. Comment: 11 pages, 6 figures. Final version, contains added discussion and modified figures to match the accepted version.Item New statistical indicator to study nonlinear gravitational clustering and structure formation(American Astronomical Society, 1996-04-22) Bagla, J. S.; Padmanabhan, T.In an = 1 universe dominated by nonrelativistic matter, velocity field and gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolve in time and these can be scaled suitably so that the constant of proportionality is unity and velocity and force field are equal. The Zeldovich approximation extends this feature beyond the linear regime, until formation of pancakes. Nonlinear clustering which takes place after the breakdown of Zeldovich approximation, breaks this relation and the mismatch between these two vectors increases as the evolution proceeds. We suggest that the difference of these two vectors could form the basis for a powerful, new, statistical indicator of nonlinear clustering. We define an indicator called velocity contrast, study its behaviour using N-Body simulations and show that it can be used effectively to delineate the regions where nonlinear clustering has taken place.We discuss several features of this statistical indicator and provide simple analytic models to understand its behaviour. Particles with velocity contrast higher than a threshold have a correlation function which is biased with respect to the original sample. This bias factor is scale dependent and tends to unity at large scales.Item Neutral hydrogen at high redshifts as a probe of structure formation – III. Radio maps from N-body simulations.(Wiley-Blackwell, 1997-04-04) Bagla, J. S.; Nath, B. B.; Padmanabhan, T.Large inhomogeneities in neutral hydrogen in the universe can be detected at redshifts z 10 using the redshifted 21cm line emission. We use cosmological N-Body simulations for dark matter and a simple model for baryonic collapse to estimate the signal expected from structures like proto-clusters of galaxies at high redshifts.We study : (i) the standard CDM model, (ii) a modified CDM model with less power at small scales, and (iii) a +CDM model in a universe with 0 + = 1. We show that it should be possible for the next generation radio telescopes to detect such structures at the redshift 3.34 with an integration of about 100 hours. We also discuss possible schemes for enhancing signal to noise ratio to detect proto-condensates at high redshifts.