Research Papers (TP)
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Item Constraints on the shape of the density spectrum from COBE and galaxy surveys(Wiley-Blackwell, 1992-10-28) Padmanabhan, T.; Narasimha, D.Item Modelling the nonlinear gravitational clustering in the expanding universe(Wiley-Blackwell, 1995-11-02) Padmanabhan, T.The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is indeed possible to understand the nonlinear clustering in terms of three well defined regimes: (1) linear regime (2) quasilinear regime which is dominated by scale-invariant radial infall and (3) nonlinear regime dominated by nonradial motions and mergers. Modelling each of these regimes separately I show how the nonlinear two point correlation function can be related to the linear correlation function in heirarchical models. This analysis leads to results which are in good agreement with numerical simulations thereby providing an explanation for numerical results. The ideas presented here will also serve as a powerful anlytical tool to investigate nonlinear clustering in different models. Several implications of the result are discussed.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 Gravitational perturbation of homogeneous collisionless dark matter(Indian Academy of Sciences, 1985-08-12) Padmanabhan, T.; Vasanthi, M. M.The effect of a perturbing mass on a homogeneous collisionless cloud of dark matter is considered in the linear approximation. It is shown by that gravitational potential can have turning points, in sharp contrast with gravitating system of finite extent. The model offers a reasonable explanation for the observed secondary maxima in the destiny distribution of rich clusters . The relevance of the model to the flatness of the rotation curves of galaxies is also discussed.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- II. Line profile of a protocluster(Wiley-Blackwell, 1994-09-05) Kumar, A.; Padmanabhan, T.; Subramanian, KandaswamyThe formation of structures at z ≤ 10.0 can be probed using the 21-cm line emisssion from the neutral hydrogen. Two of us (KS and TP, Paper I) previously computed the expected abundance of protoclusters as a function of the flux density at various redshifts, in the cold dark matter (CDM) and the hot dark matter (HDM) models. As a complement to Paper I, here we work out in detail how the H1 line profile from a spherically symmetric protocluster evolves as it decouples from Hubble expansion structures form hierarchically. Neutral hydrogen, in the small-scale clumps that from the protocluster, is the source of H1line profile in this model are typically of order 0.5-0.7 mJy, while the widths (FWHM) are of order 0.3-1.8 MHz. The major uncertainty in our calculations is the fraction of mass of the protocluster in the form of neutral hydrogen. If the neutral hydrogen fraction f is of the order of the value we have adopted (f=0.025) in our calculations or greater, then a typical protocluster could indeed be detectable by future facilities, like the Giant Metrewave Radio Telescope (GMRT) which is currently being built in India. If the neutral hydrogen fraction is much less than the value we have adopted, then a more sensitive instrument is needed to detect the H1 line emission from a typical protocluster.Item Neutral hydrogen at high redshifts as a probe of structure formation: 1. Post-COBE analysis of CDM and HDM models(Royal Astronomical Society, 1993-05-11) Subramanian, Kandaswamy; Padmanabhan, T.The structures that form in the Universe at redshifts z ≲ 10 can be detected and studied using the redshifted 21-cm line emission from neutral hydrogen. We compute the expected comoving number density, N, of protocondensates that will emit a flux higher than S, at various redshifts, in the CDM and 11DM models. The models are normalized using COBE results. Our results are compared with the present and expected future sensitivities of various telescopes for the detection of protocondensates-. In the CDM models the predicted maximum fluxes at a redshift z ≃ 3.3 are about (1.5-3) mJy and N≃(10-8-10-7)Mpc-3 . These protocondensates cannot be detected with present sensitivities, but will become detectable in the near future with improved sensitivities. At lower redshifts, the detectability of these structures critically depends on their neutral hydrogen content. In the redshift range around z≃5, individual protocondensates will not be detectable. The excess variance due to fluctuations with small density contrasts will, however, be detectable with somewhat large (say, about 60-h) integration time. At still higher redshifts, it will be virtually impossible to see any signal, even with such a large integration time. Biased CDM models predict larger fluxes, but somewhat lower abundances. Finally, the 11DM models - when normalized using COBE results - do not lead to a detectable number of sources (`pancakes') at redshifts z≳2.Item Nature and distribution of dark matter: 1. Milky way and dwarf spheroids(Indian Academy of Sciences, 1985-09-20) Padmanabhan, T.; Vasanthi, M. M.We argue that observations on Milky Way and dwarf spheroidals imply existence of individual haloes around dwarf spheroidals. If neutrions (or any other 'hot' particle) provide the dark matter then we show that: (i) Embedding of visible matter inside large (few Mpc) dark matter haloes of about 10 kpc radius around them, and have an (M/L) radio of about 100 kpc in radius. if 'cold' dark matter makes up the haloes, then no significant constraints are obtained. We discuss briefly the effect of these constraints on larger scales.