Research Papers (TP)
Permanent URI for this collectionhttp://localhost:4000/handle/11007/3
Browse
12 results
Search Results
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 What does the quasar luminosity function tell us about supermassive black hole evolution?(Wiley-Blackwell, 2006-03-13) Wyithe, J. Stuart B.; Padmanabhan, T.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 Response of distance measures to the equation of state(Wiley-Blackwell, 2003-04-05) Saini, Tarun Deep; Padmanabhan, T.; Bridle, SarahWe show that the distance measures (such as the luminosity and angular diameter distances) are linear functionals of the equation of state function w(z) of the dark energy to a fair degree of accuracy in the regimes of interest. That is, the distance measures can be expressed as a sum of (i) a constant and (ii) an integral of a weighting function multiplied by the equation of state parameter w(z). The existence of such an accurate linear response approximation has several important implications. (1) Fitting a weighted average of w(z). (2) Any polynomial (or other expansion coefficients) can also be expressed as weighted sums of the true w. (3) A replacement for the commonly used heuristic equation for the effective w, as determined by the cosmic microwave background, can be derived and the result is found to be quite close to the heuristic expression commonly used. (4) The reconstruction of w()z by Huterer & Starkman can be expressed as a matrix inversion. In each case the limitations of the linear response approximation are explored and found to be surprisingly small.Item Properties of high-redshift quasars – I. Evolution of the supermassive black hole to halo mass ratio(Wiley-Blackwell, 2005-01-17) Wyithe, J. Stuart B.; Padmanabhan, T.Item Power transfer in non-linear gravitational clustering and asymptotic universality(Wiley-Blackwell, 2006-06-13) Padmanabhan, T.; Ray, SuryadeepWe study the non-linear gravitational clustering of collisionless particles in an expanding background using an integro-differential equation for the gravitational potential. In particular, we address the question of how the non-linear mode–mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale. We show that the dynamical equation allows self-similar evolution for the gravitational potential φk(t ) in Fourier space of the form φk(t ) = F (t )D(k) where the function F(t) satisfies a second-order non-linear differential equation. We analyse the relevant solutions of this equation, thereby determining the asymptotic time evolution of the gravitational potential and density contrast. The analysis suggests that both F(t) and D(k) have well-defined asymptotic forms indicating that the power transfer leads to a universal power spectrum at late times. The analytic results are compared with numerical simulations, showing good agreement over the range at which we could test them.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.