IUCAA Preprints
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Item How to distinguish a nearly flat Universe from a flat Universe using the orientation independence of a comoving standard ruler(2001-01-20) Roukema, B. F.Several recent observations using standard rulers and standard candles now suggest, either individually or in combination, that the Universe is close to flat, i.e. that the curvature radius is about as large as the horizon radius (∼ 10h−1 Gpc) or larger. Here, a method of distinguishing an almost flat universe from a precisely flat universe using a single observational data set, without using any microwave background information, is presented. The method (i) assumes that a standard ruler should have no preferred orientation (radial versus tangential) to the observer, and (ii) requires that the (comoving) length of the standard ruler be known independently (e.g. from low redshift estimates). The claimed feature at fixed comoving length in the power spectrum of density perturbations, detected among quasars, Lyman break galaxies or other high redshift objects, would provide an adequate standard candle to prove that the Universe is curved, if indeed it is curved. For example, a combined intrinsic and measurement uncertainty of 1% in the length of the standard ruler L applied at a redshift of z = 3 would distinguish an hyperbolic (Ωm = 0.2,ΩΛ = 0.7) or a spherical (Ωm = 0.4, ΩΛ = 0.7) universe from a flat one to 1 − P > 95% confidenceItem On the comoving distance as arc-length in four dimensions(2001-08-04) Roukema, B. F.The inner product provides a conceptually and algorithmically simple method for cal- culating the comoving distance between two cosmological objects given their redshifts, right ascension and declination, and arbitrary constant curvature. The key to this is that just as a distance between two points ‘on’ the surface of the ordinary 2-sphere S2 is simply an arc-length (angle multiplied by radius) in ordinary Euclidean 3-space E3, the distance between two points ‘on’ a 3-sphere S3 (a 3-hyperboloid H3) is simply an ‘arc-length’ in Euclidean 4-space E4 (Minkowski 4-spaceM4), i.e. an ‘hyper-angle’ multiplied by the curvature radius of the 3-sphere (3-hyperboloid).Item Star formation losses due to tidal debris in `hierarchical' galaxy formation(2001-07-05) Roukema, B. F.; Ninin, S.; Devriendt, J.; et al.N-body studies have previously shown that the bottom-up hierarchical formation of dark matter haloes is not as monotonic as implicitly assumed in the Press-Schechter formalism. During and following halo mergers, matter can be ejected into tidal tails, shells or low density ‘atmospheres’ outside of the successor haloes’ viriali- sation radii (or group-finder outermost radii). The implications that the possible truncation of star formation in these tidal ‘debris’ may have for observational galaxy statistics are examined here using the ArFus N-body plus semi-analytical galaxy modelling software for standard star formation hypotheses. In the N-body simulations studied, the debris typically remain close to the successor halo and fall back into the successor haloes given sufficient time. A maximum debris loss of around 16% is found for redshift intervals of around ∆z = 0.4 at z ∼ 1, with little dependence on the matter density parameter Ω0 and the cosmological constant λ0. Upper and lower bounds on stellar losses implied by a given set of N-body simulation output data can be investi- gated by choice of the merging/identity criterion of haloes between successive N-body simulation output times. A median merging/identity criterion is defined and used to deduce an upper estimate of possible star formation and stellar population losses. A largest successor merging/identity criterion is defined to deduce an estimate which minimises stellar losses. The losses for star formation and luminosity functions are strongest for low luminosity galaxies — a likely con- sequence of the fact that the debris fraction is highest for low mass haloes — and at intermediate redshifts (1 < ∼z < ∼3). The losses in both cases are mostly around 10%-30%, have some dependence on Ω0 and negligible dependence on λ0. This upper bound on likely losses in star formation rates and stellar populations is smaller than the uncertainties in estimates of corresponding observational parameters. Hence, it may not be urgent to include a correction for this in Press-Schechter based galaxy formation models, except when statistics regarding dwarf galaxies are under study.Item Window function for non-circular beam CMB anisotropy experiment(2001-07-05) Souradeep, Tarun; Ratra, BharatWe develop computationally rapid methods to compute the window function for a cosmic microwave background anisotropy experiment with a non-circular beam which scans over large angles on the sky. To concretely illustrate these methods we compute the window function for the Python V experiment which scans over large angles on the sky with an elliptical Gaussian beam.Item Cosmological Constant and Quintessence from a Correlation Function Comoving Fine Feature in the 2dF Quasar Redshift Survey(2001-06-05) Roukema, B. F.; Mamon, G. A.Local maxima at characteristic comoving scales have previously been claimed to exist in the density perturbation spectrum at the wavenumber k = 2π/LLSS, where LLSS ∼ 100–200 h−1 Mpc (comoving), at low redshift (z < ∼0.4) for several classes of tracer objects, at z ≈ 2 among quasars, and at z ≈ 3 among Lyman break galaxies. Here, this cosmic standard ruler is sought in the “10K” initial release of the 2dF QSO Redshift Survey (2QZ-10K), by estimating the spatial two-point autocorrelation functions ξ(r) of the three-dimensional (comoving, spatial) distribution of the N = 2378 quasars in the most completely observed and “covered” sky regions of the catalogue, over the redshift ranges 0.6 < z < 1.1 (“low-z”), 1.1 < z < 1.6 (“med-z”) and 1.6 < z < 2.2 (“hi-z”). Because of the selection method of the survey and sparsity of the data, the analysis was done conservatively to avoid non-cosmological artefacts. (i) Avoiding a priori estimates of the length scales of features, local maxima in ξ(r) are found in all three different redshift ranges. The requirement that a local maximum be present in all three redshift ranges at a fixed comoving length scale implies strong, purely geometric constraints on the local cosmological parameters, in which case the length scale of the local maximum common to the three redshift ranges is 2LLSS = 244±17 h−1 Mpc. (ii) For a standard cosmological constant FLRW model, the matter density and cosmological constant are constrained to Ωm = 0.25 ± 0.10, ΩΛ = 0.65±0.25 (68% confidence), Ωm = 0.25±0.15, ΩΛ = 0.60±0.35 (95% confidence), respectively, from the 2QZ-10K alone. Independently of the type Ia supernovae data, the zero cosmological constant model (ΩΛ = 0) is rejected at the 99.7% confidence level. (iii) For an effective quintessence (wQ) model and zero curvature, wQ < −0.5 (68% confidence), wQ < −0.35 (95% confidence) are found, again from the 2QZ-10K alone. In a different analysis of a larger (but less complete) subset of the same 2QZ-10K catalogue, Hoyle et al. (2001) found a local maximum in the power spectrum to exist for widely differing choices of Ωm and ΩΛ, which is difficult to understand for a genuine large scale feature at fixed comoving length scale. A resolution of this problem and definitive results should come from the full 2QZ, which should clearly provide even more impressive constraints on fine features in density perturbation statistics, and on the local cosmological parameters Ωm, ΩΛ and wQItem Small-scale microwave background anisotropies arising from tangled promordial magnetic fields(2002-03-12) Subramanian, Kandaswamy; Barrow, John D.An inhomogeneous cosmologicalmagnetic field creates vortical perturbations that survive Silk damping onmuch smaller scales than compressionalmodes. This ensures that there is no sharp cut-off in anisotropy on arcminute scales. As we had pointed out earlier, tangled magnetic fields, if they exist, will then be a potentially important contributor to small-angular-scale cosmic microwave background radiation anisotropies. Several ongoing and new experiments are expected to probe the very small angular scales, corresponding tomultipoles with l >1000. In view of this observational focus, we revisit the predicted signals arising from primordial tangled magnetic fields, for different spectra and different cosmological parameters. We also identify a new regime, where the photon mean-free path exceeds the scale of the perturbation, which dominates the predicted signal at very high l. A scale-invariant spectrum of tangled fields which redshifts to a present value B0 = 3 × 10−9 G produces temperature anisotropies at the 10-µK level between l ∼1000 and 3000. Larger signals result if the universe is lambda- dominated, if the baryon density is larger, or if the spectral index ofmagnetic tangles is steeper, n >−3. The signalwill also have non-Gaussian statistics.We predict the distinctive formof the increased power expected in the microwave background at high l in the presence of significant tangled magnetic fields. We may be on the verge of detecting or ruling out the presence of tangledmagnetic fields that are strong enough to influence the formation of large-scale structure in the Universe.Item Measuring the geometry and topology of large scale structure using SURFGEN: Methodology and preliminary results(2002-03-22) Sheth, Jatush V.; Sahni, Varun; Shandarin, S.F.; et al.Observations of the universe reveal that matter within it clusters on a variety of scales. On scales between 10 - 100 Mpc, the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions – voids. This paper, the first in a series, presents a new ansatz which can successfully be used to determine the morphological properties of the supercluster-void network. The ansatz is based on a surface modelling scheme (SURFGEN), developed explicitly for the purpose, which generates a triangulated surface from a discrete data set representing (say) the dis- tribution of galaxies in real (or redshift) space. The triangulated surface describes, at progressively lower density thresholds, clusters of galaxies, superclusters of galaxies and voids. Four Minkowski functionals (MFs) – surface area, volume, extrinsic curva- ture and genus – describe the geometry and topology of the supercluster-void network. On a discretised and closed triangulated surface the MFs are determined using SUR- FGEN. Ratio’s of the Minkowski functionals provide us with an excellent diagnostic of three dimensional shapes of clusters, superclusters and voids. Minkowski function- als can be studied at different levels of the density contrast and therefore probe the morphology of large scale structure on a variety of length scales. Our method for determining the Minkowski functionals of a triangulated iso-density surface is tested against both simply and multiply connected eikonal surfaces such as triaxial ellipsoids and tori. The performance of our code is thereby evaluated using density distribu- tions which are pancake-like, filamentary, ribbon-like and spherical. Remarkably, the first three Minkowski functionals are computed to better than 1% accuracy while the fourth (genus) is known exactly. SURFGEN also gives very accurate results when ap- plied to Gaussian random fields. We apply SURFGEN to study morphology in three cosmological models, ΛCDM, τCDM and SCDM, at the present epoch. Geometrical properties of the supercluster-void network are found to be sensitive to the underlying cosmological parameter set. For instance, the percolating supercluster in ΛCDM turns out to be more filamentary but topologically simpler than superclusters in τCDM and SCDM. It occupies just 0.6% of the total simulation-box volume yet contains about 4% of the total mass. Our results indicate that the surface modelling scheme to calculate Minkowski functionals is accurate and robust and can successfully be used to quantify the topology and morphology of the supercluster-void network in the universe.Item Consequences on some dark energy-candidates from SN 1997ff(2001-07-28) Vishwakarma, R. G.We examine the status of various dark energy-models in light of the recently observed SN 1997ff at z ≈ 1.7. The modified data still fit a pure cosmological constant Λ or a quintessence with an equation of state similar to that of Λ. The kinematical Λ-models, Λ ∼ S−2 and Λ ∼ H2 , also fit the data reasonably well and require less dark energy density (hence more matter energy density) than is required by the constant Λ-model. However, the model Λ ∼ S−2 with low energy density becomes unphysical as it cannot accommodate higher redshift objects. We also examine an alternative explanation of the data, viz., the absorp- tion by the intervening whisker-like dust and find that the quasi-steady state model and the FRW model Ωm0 = 0.33, without any dark energy also fit the data reasonably well. We notice that the addition of SN 1997ff to the old data has worsened the fit to most of the models, except a closed FRW model with a constant Λ and a closed quintessence-model with ωφ = −0.82, and the models have started departing from each other as we go above z = 1. However, to make a clear discrimination possible, a few more supernovae with z > 1 are required. We have also calculated the age of the universe in these models and find that, in the models with a constant Λ, the expansion age is uncomfortably close to the age of the globular clusters. Quintessence-models show even lower age. The kinematical Λ-models are, however, interesting in this con- nection (especially the model Λ ∼ H2 ), which give remarkably large age of the universe.Item Size of the longest filaments in the Universe(2011-07-05) Bharadwaj, Somnath; Bhavsar, Suketu P.; Sheth, Jatush V.We analyze the filamentarity in the Las Campanas redshift survey (LCRS) and determine the length scale at which filaments are statistically significant. The largest length-scale at which filaments are statistically significant, real objects, is between 70 to 80 h−1 Mpc, for the LCRS −3o slice. Filamentary features longer than 80 h−1 Mpc, though identified, are not statistically significant; they arise from chance alignments. For the five other LCRS slices, filaments of lengths 50 h−1 Mpc to 70 h−1 Mpc are statistically significant, but not beyond. These results indicate that while individual filaments up to 80 h−1 Mpc are statistically significant, the impression of structure on larger scales is a visual effect. On scales larger than 80 h−1 Mpc the filaments interconnect by statistical chance to form the the filament-void network. The reality of the 80 h−1 Mpc features in the −3o slice make them the longest coherent features in the LCRS. While filaments are a natural outcome of gravitational instability, any numerical model attempting to describe the formation of large scale structure in the universe must produce coherent structures on scales that match these observations.Item Morphology of the supercluster-void network in /\ CDM cosmology(2011-07-05) Shandarin, S.F.; Sheth, Jatush V.; Sahni, VarunWe report here the first systematic study of the supercluster-void network in the ΛCDM concordance cosmology in which voids and superclusters are treated on an equal footing. Superclusters are defined as individual members of an over-dense excur- sion set and voids are defined as individual members of a complementary under-dense excursion set at the same density threshold. We determine the geometric, topological and morphological properties of the cosmic web at a large set of density levels by computing Minkowski functionals for every supercluster and void using SURFGEN (Sheth et al. 2003). The properties of the largest (percolating) supercluster and the complementary void are found to be very different from properties of individual su- perclusters and voids. Individual superclusters totally occupy no more than about 5% of the total volume and contain no more than 20% of mass if the largest supercluster is excluded. Likewise, individual voids totally occupy no more than 14% of volume and contain no more than 4% of mass if the largest void is excluded. Although super- clusters are more massive and voids are more voluminous the difference in maximum volumes is not greater than by an order of magnitude. The genus value of individual superclusters can be ∼ 5 while the genus of individual voids can reach ∼ 40, implying significant amount of substructure in superclusters and especially in voids. One of our main results is that large voids, as defined through the density field (read dark matter distribution) can be distinctly non-spherical.