Pixelation effects in weak lensing

Weak gravitational lensing can be used to investigate both dark matter and dark energy but requires accurate measurements of the shapes of faint, distant galaxies. Such measurements are hindered by the finite resolution and pixel scale of digital cameras. We investigate the optimum choice of pixel scale for a space-based mission, using the engineering model and survey strategy of the proposed Supernova Acceleration Probe as a baseline. We do this by simulating realistic astronomical images containing a known input shear signal and then attempting to recover the signal using the Rhodes, Refregier, & Groth algorithm. We find that the quality of shear measurement is always improved by smaller pixels. However, in practice, telescopes are usually limited to a finite number of pixels and operational life span, so the total area of a survey increases with pixel size. We therefore fix the survey lifetime and the number of pixels in the focal plane while varying the pixel scale, thereby effectively varying the survey size. In a pure trade-off for image resolution versus survey area, we find that measurements of the matter power spectrum would have minimum statistical error with a pixel scale of 0.09 '' for a 0.14 '' FWHM point-spread function (PSF). The pixel scale could be increased to similar to 0.16 '' if images dithered by exactly half-pixel offsets were always available. Some of our results do depend on our adopted shape measurement method and should be regarded as an upper limit: future pipelines may require smaller pixels to overcome systematic floors not yet accessible, and, in certain circumstances, measuring the shape of the PSF might be more difficult than those of galaxies. However, the relative trends in our analysis are robust, especially those of the surface density of resolved galaxies. Our approach thus provides a snapshot of potential in available technology, and a practical counterpart to analytic studies of pixelation, which necessarily assume an idealized shape measurement method

Developmental changes in the germinability, desiccation tolerance, hardseededness, and longevity of individual seeds of Trifolium ambiguum

Background and Aims: Using two parental clones of outcrossing Trifolium ambiguum as a potential model system, we examined how during seed development the maternal parent, number of seeds per pod, seed position within the pod, and pod position within the inflorescence influenced individual seed fresh weight, dry weight, water content, germinability, desiccation tolerance, hardseededness, and subsequent longevity of individual seeds. Methods: Near simultaneous, manual reciprocal crosses were carried out between clonal lines for two experiments. Infructescences were harvested at intervals during seed development. Each individual seed was weighed and then used to determine dry weight or one of the physiological behaviour traits. Key Results: Whilst population mass maturity was reached at 33–36 days after pollination (DAP), seed-to-seed variation in maximum seed dry weight, when it was achieved, and when maturation drying commenced, was considerable. Individual seeds acquired germinability between 14 and 44 DAP, desiccation tolerance between 30 and 40 DAP, and the capability to become hardseeded between 30 and 47 DAP. The time for viability to fall to 50 % (p50) at 60 % relative humidity and 45 °C increased between 36 and 56 DAP, when the seed coats of most individuals had become dark orange, but declined thereafter. Individual seed f. wt at harvest did not correlate with air-dry storage survival period. Analysing survival data for cohorts of seeds reduced the standard deviation of the normal distribution of seed deaths in time, but no sub-population showed complete uniformity of survival period. Conclusions: Variation in individual seed behaviours within a developing population is inherent and inevitable. In this outbreeder, there is significant variation in seed longevity which appears dependent on embryo genotype with little effect of maternal genotype or architectural factors

Evidence for Evolving Spheroidals in the Hubble Deep Fields North and South

We investigate the dispersion in the internal colours of faint spheroidals in the HDFs North and South. We find that a remarkably large fraction ~30% of the morphologically classified spheroidals with I<24 mag show strong variations in internal colour, which we take as evidence for recent episodes of star-formation. In most cases these colour variations manifest themselves via the presence of blue cores, an effect of opposite sign to that expected from metallicity gradients. Examining similarly-selected ellipticals in five rich clusters with 0.37<z<0.83 we find a significant lower dispersion in their internal colours. This suggests that the colour inhomogeneities have a strong environmental dependence being weakest in dense environments where spheroidal formation was presumably accelerated at early times. We use the trends defined by the cluster sample to define an empirical model based on a high-redshift of formation and estimate that at z~1 about half the field spheroidals must be undergoing recent episodes of star-formation. Using spectral synthesis models, we construct the time dependence of the density of star-formation. Although the samples are currently small, we find evidence for an increase in $\rho_{SFR}$ between z=0 to z=1. We discuss the implications of this rise in the context of that observed in the similar rise in the abundance of galaxies with irregular morphology. Regardless of whether there is a connection our results provide strong evidence for the continued formation of field spheroidals over 0<z<1

Towards an Algebraic Classification of Calabi-Yau Manifolds; 1, Study of K3 Spaces

We present an inductive algebraic approach to the systematic construction andclassification of generalized Calabi-Yau (CY) manifolds in different numbers ofcomplex dimensions, based on Batyrev's formulation of CY manifolds as toricvarieties in weighted complex projective spaces associated with reflexivepolyhedra. We show how the allowed weight vectors in lower dimensions may beextended to higher dimensions, emphasizing the roles of projection andintersection in their dual description, and the natural appearance ofCartan-Lie algebra structures. The 50 allowed extended four-dimensional vectorsmay be combined in pairs (triples) to form 22 (4) chains containing 90 (91) K3spaces, of which 94 are distinct, and one further K3 space is found usingduality. In the case of CY_3 spaces, pairs (triples) of the 10~270 allowedextended vectors yield 4242 (259) chains with K3 (elliptic) fibers containing730 additional K3 polyhedra. A more complete study of CY_3 spaces is left forlater work

Universal Calabi-Yau Algebra: Classification and Enumeration of Fibrations

We apply a universal normal Calabi-Yau algebra to the construction and classification of compact complex $n$-dimensional spaces with SU(n) holonomy and their fibrations. This algebraic approach includes natural extensions of reflexive weight vectors to higher dimensions and a `dual' construction based on the Diophantine decomposition of invariant monomials. The latter provides recurrence formulae for the numbers of fibrations of Calabi-Yau spaces in arbitrary dimensions, which we exhibit explicitly for some Weierstrass and K3 examples

Results from an Algebraic Classification of Calabi-Yau Manifolds

We present results from an inductive algebraic approach to the systematic construction and classification of the `lowest-level' CY3 spaces defined as zeroes of polynomial loci associated with reflexive polyhedra, derived from suitable vectors in complex projective spaces. These CY3 spaces may be sorted into `chains' obtained by combining lower-dimensional projective vectors classified previously. We analyze all the 4242 (259, 6, 1) two- (three-, four-, five-) vector chains, which have, respectively, K3 (elliptic, line-segment, trivial) fibres, yielding 174767 (an additional 6189, 1582, 199) distinct projective vectors that define reflexive polyhedra and thereby CY3 spaces, for a total of 182737. These CY3 spaces span 10827 (a total of 10882) distinct pairs of Hodge numbers h_11, h_12. Among these, we list explicitly a total of 212 projective vectors defining three-generation CY3 spaces with K3 fibrations, whose characteristics we provide

ALMA detection of [CII] 158 micron emission from a strongly lensed z=2 star-forming galaxy

Our objectives are to determine the properties of the interstellar medium (ISM) and of star-formation in typical star-forming galaxies at high redshift. Following up on our previous multi-wavelength observations with HST, Spitzer, Herschel, and the Plateau de Bure Interferometer (PdBI), we have studied a strongly lensed z=2.013 galaxy, the arc behind the galaxy cluster MACS J0451+0006, with ALMA to measure the [CII] 158 micron emission line, one of the main coolants of the ISM. [CII] emission from the southern part of this galaxy is detected at 10 $\sigma$. Taking into account strong gravitational lensing, which provides a magnification of $\mu=49$, the intrinsic lensing-corrected [CII]158 micron luminosity is $L(CII)=1.2 \times 10^8 L_\odot$. The observed ratio of [CII]-to-IR emission, $L(CII)/L(FIR) \approx (1.2-2.4) \times 10^{-3}$, is found to be similar to that in nearby galaxies. The same also holds for the observed ratio $L(CII)/L(CO)=2.3 \times 10^3$, which is comparable to that of star-forming galaxies and active galaxy nuclei (AGN) at low redshift. We utilize strong gravitational lensing to extend diagnostic studies of the cold ISM to an order of magnitude lower luminosity ($L(IR) \sim (1.1-1.3) \times 10^{11} L_\odot$) and SFR than previous work at high redshift. While larger samples are needed, our results provide evidence that the cold ISM of typical high redshift galaxies has physical characteristics similar to normal star forming galaxies in the local Universe.Comment: 5 pages, 4 figures. Accepted for publication in Astronomy & Astrophysics, Letter

Hubble flow variance and the cosmic rest frame

We characterize the radial and angular variance of the Hubble flow in the COMPOSITE sample of 4534 galaxies, on scales in which much of the flow is in the nonlinear regime. With no cosmological assumptions other than the existence of a suitably averaged linear Hubble law, we find with decisive Bayesian evidence (ln B >> 5) that the Hubble constant averaged in independent spherical radial shells is closer to its asymptotic value when referred to the rest frame of the Local Group, rather than the standard rest frame of the Cosmic Microwave Background. An exception occurs for radial shells in the range 40/h-60/h Mpc. Angular averages reveal a dipole structure in the Hubble flow, whose amplitude changes markedly over the range 32/h-62/h Mpc. Whereas the LG frame dipole is initially constant and then decreases significantly, the CMB frame dipole initially decreases but then increases. The map of angular Hubble flow variation in the LG rest frame is found to coincide with that of the residual CMB temperature dipole, with correlation coefficient -0.92. These results are difficult to reconcile with the standard kinematic interpretation of the motion of the Local Group in response to the clustering dipole, but are consistent with a foreground non-kinematic anisotropy in the distance-redshift relation of 0.5% on scales up to 65/h Mpc. Effectively, the differential expansion of space produced by nearby nonlinear structures of local voids and denser walls and filaments cannot be reduced to a local boost. This hypothesis suggests a reinterpretation of bulk flows, which may potentially impact on calibration of supernovae distances, anomalies associated with large angles in the CMB anisotropy spectrum, and the dark flow inferred from the kinematic Sunyaev-Zel'dovich effect. It is consistent with recent studies that find evidence for a non-kinematic dipole in the distribution of distant radio sources.Comment: 37 pages, 9 tables, 13 figures; v2 adds extensive new analysis (including additional subsections, tables, figures); v3 adds a Monte Carlo analysis (with additional table, figure) which further tightens the statistical robustness of the dipole results; v4 adds further clarifications, small corrections, references and discussion of Planck satellite results; v5 typos fixed, matches published versio