Lensing magnification effects on the cosmic shear statistics

Gravitational lensing causes a correlation between a population of foreground large-scale structures and the observed number density of the background distant galaxies as a consequence of the flux magnification and the lensing area distortion. This correlation has not been taken into account in calculations of the theoretical predictions of the cosmic shear statistics but may cause a systematic error in a cosmic shear measurement. We examine its impact on the cosmic shear statistics using the semi-analytic approach. We find that the lensing magnification has no practical influence on the cosmic shear variance. Exploring the possible shapes of the redshift distribution of source galaxies, we find that the relative amplitude of the effect on the convergence skewness is 3 per cent at most.     

Are there sextuplet and octuplet image systems?

We study gravitational lensing by the family of scale-free galaxies with flat rotation curves. The models are defined by a shape function, which prescribes the radius of the isophote as a function of the position angle from the major axis. The critical curves are analytic, while the caustic network is reducible to a simple quadrature. The cusps are always located at the turning points of the shape function. We show that the models with exactly elliptic isophotes never admit butterfly or swallowtail cusps and so have at most four (or five) images. Higher order imaging is brought about by deviations of the isophotes from pure ellipses, such as pointedness caused by embedded discs or boxiness caused by recent merging. The criteria for the onset of sextuple and octuple imaging can be calculated analytically in terms of the ellipticity ε and the fourth-order Fourier coefficients ( a ₄ and b ₄) used by observers to parametrize the isophote shapes. The six or eight images are arranged roughly in a circle, which appears as an incomplete Einstein ring if inadequately resolved. Using data on the shapes of elliptical galaxies and merger remnants, we estimate that ∼1 per cent of all multiply imaged quasars may be sextuplet systems or higher. Forthcoming satellites such as the Global Astrometric Interferometer for Astrophysics ( GAIA ) will provide data sets of ∼4000 multiply imaged systems, and so ∼40 will show sextuple imaging or higher.     

How useful are ‘millipede’ and other similar porphyroblast microstructures for determining synmetamorphic deformation histories?

ABSTRACT Oppositely concave microfolds (OCMs) in and adjacent to porphyroblasts can be classified into five nongenetic types. Type 1 OCMs are found in sections through porphyroblasts with spiral-shaped inclusion trails cut parallel to the spiral axes, and commonly show closed foliation loops. Type 2 OCMs, commonly referred to as ‘millipede’ microstructure, are highly symmetrical, the foliation folded into OCMs being approximately perpendicular to the overprinting foliation. Type 3 OCMs are similar to Type 2, but are asymmetrical, the foliation folded into OCMs being variably oblique to the overprinting foliation. Type 4 OCMs are highly asymmetrical, only one foliation is present, and this foliation is parallel to the local shear plane. Type 5 OCMs result from porphyroblast growth over a microfold interference pattern. Types 1 and 2 are commonly interpreted as indicating highly noncoaxial and highly coaxial bulk deformation paths, respectively, during porphyroblast growth. However, theoretically they can form by any deformation path intermediate between bulk coaxial shortening and bulk simple shearing. Given particular initial foliation orientation and timing of porphyroblast growth, Type 3 OCMs can also form during these intermediate deformation paths, and are commonly found in the same rocks as Type 2 OCMs. Type 4 OCMs may indicate highly noncoaxial deformation during porphyroblast growth, but may be difficult to distinguish from Type 3 OCMs. Thus, Types 1–3 (and possibly 4) reflect the finite strain state, giving no information about the rotational component of the deformation(s) responsible for their formation. Furthermore, there is a lack of unequivocal independent evidence for the degree of noncoaxiality of deformation (s) during the growth of porphyroblasts containing OCMs. Type 2 OCMs that occur independently of porphyroblasts or other rigid objects might indicate highly coaxial bulk shortening, but there is a lack of supporting physical or computer modelling. It is possible that microstructures in the matrix around OCMs formed during highly noncoaxial and highly coaxial deformation histories might have specific characteristics that allow them to be distinguished from one another. However, determining degrees of noncoaxiality from rock fabrics is a major, longstanding problem in structural geology.     

SHRIMP U–Pb ages of ultrahigh-pressure and retrograde metamorphism of gneisses, south-western Sulu terrane, eastern China

Laser Raman spectroscopy and cathodoluminescence (CL) images reveal that most zircon separated from paragneiss and orthogneiss in drillhole CCSD‐PP2 at Donghai, south‐western Sulu terrane, retain low‐P mineral‐bearing inherited cores, ultrahigh‐pressure (UHP) mineral‐bearing mantles and low‐P mineral‐bearing (e.g. quartz) rims. SHRIMP U–Pb analyses of these zoned zircon identify three discrete and meaningful age groups: Proterozoic protolith ages (> 680 Ma) are recorded in the inherited cores, the UHP metamorphic event in the coesite‐bearing mantles occurred at 231 ± 4 Ma, and the late amphibolite facies retrogressive overprint in the quartz‐bearing rims was at 211 ± 4 Ma. Thus, Neoproterozoic supracrustal protoliths of the Sulu UHP rocks were subducted to mantle depths in the Middle Triassic, and exhumed to mid‐crustal levels in the Late Triassic. The exhumation rate deduced from the SHRIMP data and metamorphic P–T conditions is 5.0 km Ma^?1. Exhumation of the Sulu UHP terrane may have resulted from buoyancy forces after slab break‐off at mantle depths.     

On the probability of microlensing in gamma-ray burst afterglows

The declining light curve of the optical afterglow of gamma-ray burst (GRB) GRB000301C showed rapid variability with one particularly bright feature at about t − t ₀=3.8 d. This event was interpreted as gravitational microlensing by Garnavich, Loeb & Stanek and subsequently used to derive constraints on the structure of the GRB optical afterglow. In this paper, we use these structural parameters to calculate the probability of such a microlensing event in a realistic scenario, where all compact objects in the universe are associated with observable galaxies. For GRB000301C at a redshift of z =2.04, the a posteriori probability for a microlensing event with an amplitude of Δ m 0.95 mag (as observed) is 0.7 per cent (2.7 per cent) for the most plausible scenario of a flat Λ-dominated Friedmann–Robertson–Walker (FRW) universe with Ω_m=0.3 and a fraction f ∗=0.2 (1.0) of dark matter in the form of compact objects. If we lower the magnification threshold to Δ m 0.10 mag, the probabilities for microlensing events of GRB afterglows increase to 17 per cent (57 per cent). We emphasize that this low probability for a microlensing signature of almost 1 mag does not exclude that the observed event in the afterglow light curve of GRB000301C was caused by microlensing, especially in light of the fact that a galaxy was found within 2 arcsec from the GRB. In that case, however, a more robust upper limit on the a posteriori probability of ≈5 per cent is found. It does show, however, that it will not be easy to create a large sample of strong GRB afterglow microlensing events for statistical studies of their physical conditions on microarcsec scales.     

On the distribution of haloes, galaxies and mass

The stochasticity in the distribution of dark haloes in the cosmic density field is reflected in the distribution function   P _V ( N _h| δ _m)  , which gives the probability of finding N _h haloes in a volume V with mass density contrast δ _m. We study the properties of this function using high-resolution N -body simulations, and find that   P _V ( N _h| δ _m)  is significantly non-Poisson. The ratio between the variance and the mean goes from ∼1 (Poisson) at  1+ δ _m≪1  to <1 (sub-Poisson) at  1+ δ _m∼1  to >1 (super-Poisson) at  1+ δ _m≫1  . The mean bias relation is found to be well described by halo bias models based on the Press–Schechter formalism. The sub-Poisson variance can be explained as a result of halo exclusion, while the super-Poisson variance at high δ _m may be explained as a result of halo clustering. A simple phenomenological model is proposed to describe the behaviour of the variance as a function of δ _m. Galaxy distribution in the cosmic density field predicted by semi-analytic models of galaxy formation shows similar stochastic behaviour. We discuss the implications of the stochasticity in halo bias to the modelling of higher order moments of dark haloes and of galaxies.