## Wednesday, January 13, 2010

### Where does the element Beryllium come from?

Beryllium abundances and the formation of the halo and the thick disk
The single stable isotope of beryllium is a pure product of cosmic-ray spallation in the ISM. Assuming that the cosmic-rays are globally transported across the Galaxy, the beryllium production should be a widespread process and its abundance should be roughly homogeneous in the early-Galaxy at a given time. Thus, it could be useful as a tracer of time. In an investigation of the use of Be as a cosmochronometer and of its evolution in the Galaxy, we found evidence that in a log(Be/H) vs. [alpha/Fe] diagram the halo stars separate into two components. One is consistent with predictions of evolutionary models while the other is chemically indistinguishable from the thick-disk stars. This is interpreted as a difference in the star formation history of the two components and suggests that the local halo is not a single uniform population where a clear age-metallicity relation can be defined. We also found evidence that the star formation rate was lower in the outer regions of the thick disk, pointing towards an inside-out formation.

### dark matter and gravitational lensing

The dark matter of gravitational lensing
We review progress in understanding dark matter by astrophysics, and particularly via the effect of gravitational lensing. Evidence from many different directions now implies that five sixths of the material content of the universe is in this mysterious form, separate from and beyond the ordinary "baryonic" particles in the standard model of particle physics. Dark matter appears not to interact via the electromagnetic force, and therefore neither emits nor reflects light. However, it definitely does interact via gravity, and has played the most important role in shaping the Universe on large scales. The most successful technique with which to investigate it has so far been gravitational lensing. The curvature of space-time near any gravitating mass (including dark matter) deflects passing rays of light - observably shifting, distorting and magnifying the images of background galaxies. Measurements of such effects currently provide constraints on the mean density of dark matter, and its density relative to baryonic matter; the size and mass of individual dark matter particles; and its cross section under various fundamental forces.

Weak lensing, dark matter and dark energy
Weak gravitational lensing is rapidly becoming one of the principal probes of dark matter and dark energy in the universe. In this brief review we outline how weak lensing helps determine the structure of dark matter halos, measure the expansion rate of the universe, and distinguish between modified gravity and dark energy explanations for the acceleration of the universe. We also discuss requirements on the control of systematic errors so that the systematics do not appreciably degrade the power of weak lensing as a cosmological probe.

Microlensing as a probe of the Galactic structure; 20 years of microlensing optical depth studies
Microlensing is now a very popular observational astronomical technique. The investigations accessible through this effect range from the dark matter problem to the search for extra-solar planets. In this review, the techniques to search for microlensing effects and to determine optical depths through the monitoring of large samples of stars will be described. The consequences of the published results on the knowledge of the Milky-Way structure and its dark matter component will be discussed. The difficulties and limitations of the ongoing programs and the perspectives of the microlensing optical depth technique as a probe of the Galaxy structure will also be detailed.

### the Milky Way's dwarfs

Determining orbits for the Milky Way's dwarfs
We calculate orbits for the Milky Way dwarf galaxies with proper motions, and compare these to subhalo orbits in a high resolution cosmological simulation. We use the simulation data to assess how well orbits may be recovered in the face of measurement errors, a time varying triaxial gravitational potential, and satellite-satellite interactions. For present measurement uncertainties, we recover the apocentre r_a and pericentre r_p to ~40%. With improved data from the Gaia satellite we should be able to recover r_a and r_p to ~14%, respectively. However, recovering the 3D positions and orbital phase of satellites over several orbits is more challenging. This owes primarily to the non-sphericity of the potential and satellite interactions during group infall. Dynamical friction, satellite mass loss and the mass evolution of the main halo play a more minor role in the uncertainties.
We apply our technique to nine Milky Way dwarfs with observed proper motions. We show that their mean apocentre is lower than the mean of the most massive subhalos in our cosmological simulation, but consistent with the most massive subhalos that form before z=10. This lends further support to the idea that the Milky Way's dwarfs formed before reionisation.

### the Dirac Belt Trick

Understanding Quaternions and the Dirac Belt Trick
The Dirac belt trick is often employed in physics classrooms to show that a $2\pi$ rotation is not topologically equivalent to the absence of rotation whereas a $4\pi$ rotation is, mirroring a key property of quaternions and their isomorphic cousins, spinors. The belt trick can leave the student wondering if a real understanding of quaternions and spinors has been achieved, or if the trick is just an amusing analogy. The goal of this paper is to demystify the belt trick and to show that it implies an underlying \emph{four-dimensional} parameter space for rotations that is simply connected. An investigation into the geometry of this four-dimensional space leads directly to the system of quaternions, and to an interpretation of three-dimensional vectors as the generators of rotations in this larger four-dimensional world. The paper also shows why quaternions are the natural extension of complex numbers to four dimensions.