On the Probability Distributions of Ellipticity

In this paper we derive an exact full expression for the 2D probability distribution of the ellipticity of an object measured from data, only assuming Gaussian noise in pixel values. This is a generalisation of the probability distribution for the ratio of single random variables, that is well-known, to the multivariate case. This expression is derived within the context of the measurement of weak gravitational lensing from noisy galaxy images. We find that the third flattening, or epsilon-ellipticity, has a biased maximum likelihood but an unbiased mean; and that the third eccentricity, or normalised polarisation chi, has both a biased maximum likelihood and a biased mean. The very fact that the bias in the ellipticity is itself a function of the ellipticity requires an accurate knowledge of the intrinsic ellipticity distribution of the galaxies in order to properly calibrate shear measurements. We use this expression to explore strategies for calibration of biases caused by measurement processes in weak gravitational lensing. We find that upcoming weak lensing surveys like KiDS or DES require calibration fields of order of several square degrees and 1.2 magnitude deeper than the wide survey in order to correct for the noise bias. Future surveys like Euclid will require calibration fields of order 40 square degree and several magnitude deeper than the wide survey. We also investigate the use of the Stokes parameters to estimate the shear as an alternative to the ellipticity. We find that they can provide unbiased shear estimates at the cost of a very large variance in the measurement. The python code used to compute the distributions presented in the paper and to perform the numerical calculations are available on request.Comment: 24 pages, 18 figures, 2 Tables. Accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journa

Implications for the missing low-mass galaxies (satellites) problem from cosmic shear

The number of observed dwarf galaxies, with dark matter mass $\lesssim 10^{11}$ M$_{\odot}$ in the Milky Way or the Andromeda galaxy does not agree with predictions from the successful $\Lambda$CDM paradigm. To alleviate this problem a suppression of dark matter clustering power on very small scales has been conjectured. However, the abundance of dark matter halos outside our immediate neighbourhood (the Local Group) seem to agree with the $\Lambda$CDM--expected abundance. Here we connect these problems to observations of weak lensing cosmic shear, pointing out that cosmic shear can make significant statements about the missing satellites problem in a statistical way. As an example and pedagogical application we use recent constraints on small-scales power suppression from measurements of the CFHTLenS data. We find that, on average, in a region of $\sim$Gpc$^3$ there is no significant small-scale power suppression. This implies that suppression of small-scale power is not a viable solution to the `missing satellites problem' or, alternatively, that on average in this volume there is no `missing satellites problem' for dark matter masses $\gtrsim 5 \times 10^9$ M$_{\odot}$. Further analysis of current and future weak lensing surveys will probe much smaller scales, $k > 10h$ Mpc$^{-1}$ corresponding roughly to masses $M < 10^9 M_{\odot}$.Comment: Matches published version in MNRAS Letters; no change

Report on trial of SatScan tray scanner system by SmartDrive Ltd.

Smartdrive Ltd. has developed a prototype imaging system, SatScan, that captures digitised images of large areas while keeping smaller objects in focus at very high resolution. The system was set up in the Sackler Biodiversity Imaging laboratory of Natural History Museum on March 8, 2010 for a one-month trial. A series of projects imaging parts of the entomological, botanical and palaeoentomological collection were conducted to assess the systems utility for museum collection management and biodiversity research. The technical and practical limitations of the system were investigated as part of this process

Can we measure the neutrino mass hierarchy in the sky?

Cosmological probes are steadily reducing the total neutrino mass window, resulting in constraints on the neutrino-mass degeneracy as the most significant outcome. In this work we explore the discovery potential of cosmological probes to constrain the neutrino hierarchy, and point out some subtleties that could yield spurious claims of detection. This has an important implication for next generation of double beta decay experiments, that will be able to achieve a positive signal in the case of degenerate or inverted hierarchy of Majorana neutrinos. We find that cosmological experiments that nearly cover the whole sky could in principle distinguish the neutrino hierarchy by yielding 'substantial' evidence for one scenario over the another, via precise measurements of the shape of the matter power spectrum from large scale structure and weak gravitational lensing.Comment: Submitted to JCA