On a systematic bias in surface brightness fluctuations based distances due to gravitational microlensing

The effect of gravitational microlensing on the determination of extragalactic distances using the surface brightness fluctuations (SBF) technique is considered and a method to calculate SBF amplitudes in the presence of microlensing is presented. With a simple approximation for the magnification power spectrum at low optical depth, the correction to the SBF-based luminosity distance is calculated. The results suggest the effect can be safely neglected at present but may become important for SBF-based Hubble diagrams at luminosity distances of about 1 Gpc and beyond.     

Background-field effects in astrometric microlensing

We consider the motion of the image of a distant radiation source microlensed by one and many point masses in the presence of an external background field, which produces a shear in the lens equation. The trajectories of the image brightness centroid (BC) in a Chang-Refsdal lens are very sensitive to the magnitude of the shear and to the direction of motion of the microlenses, allowing these parameters to be unambiguously determined from the BC motion. Stochastic motions of the BC for an extended source are simulated in a problem with a large number of randomly arranged microlenses. We derive dependences of the root-mean-square variations in BC velocity on microlense density, on external shear, and on the continuous component of the mass density, which may be related to dark matter in extragalactic lenses.     

Hydrodynamic modelling of some metamorphic processes

The P–T paths for metamorphic complexes from the Precambrian shields and fold belts of different ages may result from advection, i.e. one-cycle convective processes in the lithosphere. This conclusion has been exemplified by the metamorphic evolution of several well-known complexes, for which an advective model can be successfully applied. Numerical simulations of the above processes in terms of Newtonian rheology by using a two-dimensional finite element program have been conducted.
Two representative models for intracontinental gravitational ordering initiated presumably by mantle activity are considered: (i) a thermally activated multi-layered rhythmic sequence and (ii) huge rising diapiars causing circulation, in which crustal lithologies underwent high- P metamorphism (above 10–15 kbar) and subsequent ascent toward the Earth's surface.     

Giant cluster arcs as a constraint on the scattering cross-section of dark matter

We carry out ray tracing through five high-resolution simulations of a galaxy cluster, to study how its ability to produce giant gravitationally lensed arcs is influenced by the collision cross-section of its dark matter. In three cases typical dark matter particles in the cluster core undergo between 1 and 100 collisions per Hubble time; two more explore the long ('collisionless') and short ('fluid') mean free path limits. We study the size and shape distributions of arcs and compute the cross-section for producing 'extreme' arcs of various sizes. Even a few collisions per particle modifies the core structure enough to destroy the ability of the cluster to produce long, thin arcs. For larger collision frequencies the cluster must be scaled up to unrealistically large masses before it regains the ability to produce giant arcs. None of our models with self-interacting dark matter (except the 'fluid' limit) is able to produce radial arcs; even the case with the smallest scattering cross-section must be scaled to the upper limit of observed cluster masses before it produces radial arcs. Apparently the elastic collision cross-section of dark matter in clusters must be very small, below 0.1 cm² g⁻¹, to be compatible with the observed ability of clusters to produce both radial arcs and giant arcs.     

The gravitational potential of a homogeneous polyhedron or don't cut corners

A polyhedron can model irregularly shaped objects such as asteroids, comet nuclei, and small planetary satellites. With minor effort, such a model can incorporate important surface features such as large craters. Here we develop closed-form expressions for the exterior gravitational potential and acceleration components due to a constant-density polyhedron. An equipotential surface of Phobos is illustrated.     

The stochastic background of gravitational waves from neutron star formation at cosmological distances

We investigate the stochastic gravitational wave background that results from neutron star birth throughout the Universe. The neutron star birth rate, as a function of redshift, is calculated using an observation-based model for the evolving star formation rate, together with an estimate of the rate of core-collapse supernovae in the nearby Universe and an estimate of the neutron star/black hole branching ratio. Using three sample waveforms, based on numerical models of stellar core collapse by Zwerger & Müller, the spectral flux density, spectral strain, spectral energy density and duty cycle of the background have been computed. Our results show, contrary to recent claims, that the spectrum of the stochastic background clearly reflects the different physics in the core-collapse models. For a star formation model that is corrected for dust extinction, the neutron star formation rate throughout the Universe is high enough to result in a nearly continuous background of gravitational waves, with spectral features that can be related to emission mechanisms.