Rates for Color Shifted Microlensing Events

If the objects responsible for gravitational microlensing (ML) of Galactic-bulge stars are faint dwarfs, then blended light from the lens will distort the shape of the ML light curve and shift the color of the observed star during the event. The resolution in current surveys is not accurate enough to observe this effect, but it should be detected with frequent and precise followup observations. We calculate the expected rates for ML events where the shape distortions will be observable by such followup observations, assuming that the lenses are ordinary main-sequence stars in a bar and in the disk. We study the dependence of the rates for color-shifted (CS) events on the frequency of followup observations and on the precision of the photometry for a variety of waveband pairings. We find that for hourly observations in $B$ and $K$ with typical photometric errors of 0.01 mag, 28\% of the events where a main-sequence bulge star is lensed, and 7\% of the events where the source is a bulge giant, will give rise to a measurable CS at the 95\% confidence level. For observations in $V$ and $I$, the fractions become 18\% and 5\%, respectively, but may be increased to 40\% and 13\% by improved photometric accuracy and increased sampling frequency. We outline how the mass, distance, and transverse speed of the lens can be obtained, giving examples of typical errors. We discuss how CS events can be distinguished from events where the source is blended with a binary companion.Comment: 36 pages, uuencoded postscript fil

Two-dimensional Packing in Prolate Granular Materials

We investigate the two-dimensional packing of extremely prolate (aspect ratio $\alpha=L/D>10$) granular materials, comparing experiments with Monte-Carlo simulations. The average packing fraction of particles with aspect ratio $\alpha=12$ is $0.68\pm0.03$. We quantify the orientational correlation of particles and find a correlation length of two particle lengths. The functional form of the decay of orientational correlation is the same in both experiments and simulations spanning three orders of magnitude in aspect ratio. This function decays over a distance of two particle lengths. It is possible to identify voids in the pile with sizes ranging over two orders of magnitude. The experimental void distribution function is a power law with exponent $-\beta=-2.43\pm0.08$. Void distributions in simulated piles do not decay as a power law, but do show a broad tail. We extend the simulation to investigate the scaling at very large aspect ratios. A geometric argument predicts the pile number density to scale as $\alpha^{-2}$. Simulations do indeed scale this way, but particle alignment complicates the picture, and the actual number densities are quite a bit larger than predicted.Comment: 6 pages + 10 ps/eps figure

Galactosynthesis: halo histories, star formation and discs

We investigate the effects of a variety of ingredients that must enter into a realistic model for disc galaxy formation, focusing primarily on the Tully–Fisher (TF) relation and its scatter in several wavebands. In particular, we employ analytic distributions for halo formation redshifts and halo spins, empirical star formation rates and initial mass functions, realistic stellar populations, and chemical evolution of the gas. Our main findings are as follows. (a) The slope, normalization and scatter of the TF relation across various wavebands are determined largely by the parent halo properties as dictated by the initial conditions, but are also influenced by star formation in the disc. (b) TF scatter in this model is due primarily to the spread in formation redshifts. The scatter can be measurably reduced by chemical evolution, and also by the weak anticorrelation between peak height and spin. (c) Multiwavelength constraints can be important in distinguishing between models that appear to fit the TF relation in I or K. (d) Assuming passive disc evolution, successful models seem to require that the bulk of disc formation cannot occur too early (z>2–3) or too late (z<0.2), and are inconsistent with high values of Ω₀. (e) A simple, realistic model with the above ingredients, and fewer free parameters than typical semi-analytic models, can reasonably reproduce the observed z=0 TF relation in all bands (B, R, I and K), as well as the observed B-band surface brightness–magnitude relation. In such a model, the near-infrared TF relation at z=1 is similar to that at z=0, while bluer bands show a markedly steeper TF slope at high redshift, consistent with limited current data. The remarkable agreement with observations suggests that the amount of gas that is expelled or poured into a disc galaxy may be small (though small fluctuations might serve to align B-band predictions better with observations), and that the specific angular momentum of the baryons should roughly equal that of the halo; there is little room for angular momentum transfer. In Appendix A we present analytic fits to stellar population synthesis models