Lensing Properties of Cored Galaxy Models

A method is developed to evaluate the magnifications of the images of galaxies with lensing potentials stratified on similar concentric ellipses. A simple contour integral is provided which enables the sums of the magnifications of even parity or odd parity or the central image to be easily calculated. The sums for pairs of images vary considerably with source position, while the signed sums can be remarkably uniform inside the tangential caustic in the absence of naked cusps. For a family of models in which the potential is a power-law of the elliptic radius, the number of visible images is found as a function of flattening, external shear and core radius. The magnification of the central image depends on the core radius and the slope of the potential. For typical source and lens redshifts, the missing central image leads to strong constraints; the mass distribution in the lensing galaxy must be nearly cusped, and the cusp must be isothermal or stronger. This is in accord with the cuspy cores seen in high resolution photometry of nearby, massive, early-type galaxies, which typically have the surface density falling like distance^{-1.3} outside a break radius of a few hundred parsecs. Cuspy cores by themselves can provide an explanation of the missing central images. Dark matter at large radii may alter the slope of the projected density; provided the slope remains isothermal or steeper and the break radius remains small, then the central image remains unobservable. The sensitivity of the radio maps must be increased fifty-fold to find the central images in abundance.Comment: 42 pages, 11 figures, ApJ in pres

No Need for Dark Matter in Galaxies?

Unhappily, there has been a maelstrom of problems for dark matter theories over the last few years and many serious difficulties still have no resolution in sight. This article reviews the evidence for dark matter in galaxies. The haloes built up by hierarchical merging in dark matter cosmogonies are cusped and dominated by dark matter at the center. Evidence from the microlensing optical depth towards Baade's Window and from dynamical modelling of the Galactic bar already suggests that the Galactic halo is not cusped. Similarly, evidence from the stability of unbarred disk galaxies, as well as the survival of fast bars in barred galaxies, suggests that the this result holds good more generally. Judged on the data from galactic scales alone, the case for dark matter is weak and non-standard theories of gravity provide a better description. Of course, non-standard theories of gravity have their own problems, but not on galactic scales.Comment: 8 pages, invited review for "IDM 2000: Third International Workshop on the Identification of Dark Matter", ed. N. Spooner (World Scientific

Microlensing Maps for the Galactic Bulge

Microlensing maps -- that is, contours of equal numbers of events per $10^6$ source stars -- are provided for the inner Galaxy under two alternative hypotheses : (1) the bulge is an oblate axisymmetric spheroid or (2) the bulge is a prolate bar. Oblate spheroids yield a total of $\sim 12$ events per year per $10^6$ stars at Baade's Window ($\sim 15$ events if the disk is maximal). The event rate is slightly lower for prolate bars viewed at $\sim 45^\circ$ and the maps have a characteristic asymmetry between positive and negative longitudes. Prolate bars can yield mild amplifications of the event rate if viewed almost down the long axis. The disk provides the dominant lensing population on the bulge major axis for |\ell | \gta 6^\circ. Measurements of the rate at major axis windows can test for disk dark matter or maximal disk models.Comment: 12 pages, Late

Axisymmetric Self-Similar Equilibria of Self-Gravitating Isothermal Systems

All axisymmetric self-similar equilibria of self-gravitating, rotating, isothermal systems are identified by solving the nonlinear Poisson equation analytically. There are two families of equilibria: (1) Cylindrically symmetric solutions in which the density varies with cylindrical radius as R^(-alpha), with 0 <= alpha <= 2. (2) Axially symmetric solutions in which the density varies as f(theta)/r^2, where `r' is the spherical radius and `theta' is the co-latitude. The singular isothermal sphere is a special case of the latter class with f(theta)=constant. The axially symmetric equilibrium configurations form a two-parameter family of solutions and include equilibria which are surprisingly asymmetric with respect to the equatorial plane. The asymmetric equilibria are, however, not force-free at the singular points r=0, infinity, and their relevance to real systems is unclear. For each hydrodynamic equilibrium, we determine the phase-space distribution of the collisionless analog.Comment: 13 pages, 7 figures, uses emulateapj.sty. Submitted to Ap

RIP: The Macho Era (1974-2004)

This article reviews the life and death of a scientific theory.Comment: 10 pages, 3 figures, invited review for "The Fifth International Workshop on the Identification of Dark Matter", eds N. Spooner, V. Kudryavtsev (World Scientific, Singapore

A Dipole on the Sky: Predictions for Hypervelocity Stars from the Large Magellanic Cloud

We predict the distribution of hypervelocity stars (HVSs) ejected from the Large Magellanic Cloud (LMC), under the assumption that the dwarf galaxy hosts a central massive black hole (MBH). For the majority of stars ejected from the LMC the orbital velocity of the LMC has contributed a significant fraction of their galactic rest frame velocity, leading to a dipole density distribution on the sky. We quantify the dipole using spherical harmonic analysis and contrast with the monopole expected for HVSs ejected from the Galactic Center. There is a tendril in the density distribution that leads the LMC which is coincident with the well-known and unexplained clustering of HVSs in the constellations of Leo and Sextans. Our model is falsifiable, since it predicts that Gaia will reveal a large density of HVSs in the southern hemisphere.Comment: 6 pages, ApJ (Letters), in pres