The caustic ring singularity

I investigate the caustics produced by the fall of collisionless dark matter in and out of a galaxy in the limit of negligible velocity dispersion. The outer caustics are spherical shells enveloping the galaxy. The inner caustics are rings. These are located near where the particles with the most angular momentum are at their distance of closest approach to the galactic center. The surface of a caustic ring is a closed tube whose cross-section is a $D_{-4}$ catastrophe. It has three cusps amongst which exists a discrete $Z_3$ symmetry. A detailed analysis is given in the limit where the flow of particles is axially and reflection symmetric and where the transverse dimensions of the ring are small compared to the ring radius. Five parameters describe the caustic in that limit. The relations between these parameters and the initial velocity distribution of the particles are derived. The structure of the caustic ring is used to predict the shape of the bump produced in a galactic rotation curve by a caustic ring lying in the galactic plane.Comment: 34 pages, 10 figures, a minor comment has been adde

Evidence for universal structure in galactic halos

The late infall of dark matter onto a galaxy produces structure (such as caustics) in the distribution of dark matter in the halo. We argue that such structure is likely to occur generically on length scales proportional to $l \sim t_0 v_{rot}$, where $t_0$ is the age of the universe and $v_{rot}$ is the rotation velocity of the galaxy. A set of 32 extended galactic rotation curves is analyzed. For each curve, the radial coordinate is rescaled according to $r\to \tilde r \equiv r (v_0 / v_{rot})$, where we choose $v_0 = 220 km/s$. A linear fit to each rescaled rotation curve is subtracted, and the residuals are binned and averaged. The sample shows significant features near $\tilde r = 40 kpc$ and $\tilde r = 20 kpc$. This is consistent with the predictions of the self-similar caustic ring model of galactic halos.Comment: 4 pages, LaTeX, 1 epsf figur

The velocity peaks in the cold dark matter spectrum on Earth

The cold dark matter spectrum on earth is expected to have peaks in velocity space. We obtain estimates for the sizes and locations of these peaks. To this end we have generalized the secondary infall model of galactic halo formation to include angular momentum of the dark matter particles. This new model is still spherically symmetric and it has self-similar solutions. Our results are relevant to direct dark matter search experiments.Comment: 12 pages including 1 table and 4 figures, LaTeX, REVTEX 3.0 versio

The secondary infall model of galactic halo formation and the spectrum of cold dark matter particles on Earth

The spectrum of cold dark matter particles on Earth is expected to have peaks in velocity space associated with particles which are falling onto the Galaxy for the first time and with particles which have fallen in and out of the Galaxy only a small number of times in the past. We obtain estimates for the velocity magnitudes and the local densities of the particles in these peaks. To this end we use the secondary infall model of galactic halo formation which we have generalized to take account of the angular momentum of the dark matter particles. The new model is still spherically symmetric and it admits self-similar solutions. In the absence of angular momentum, the model produces flat rotation curves for a large range of values of a parameter $\epsilon$ which is related to the spectrum of primordial density perturbations. We find that the presence of angular momentum produces an effective core radius, i.e. it makes the contribution of the halo to the rotation curve go to zero at zero radius. The model provides a detailed description of the large scale properties of galactic halos including their density profiles, their extent and total mass. We obtain predictions for the kinetic energies of the particles in the velocity peaks and estimates for their local densities as functions of the amount of angular momentum, the age of the universe and $\epsilon$.Comment: LaTeX, 39 pages including 18 figure

TreePM Method for Two-Dimensional Cosmological Simulations

We describe the two-dimensional TreePM method in this paper. The 2d TreePM code is an accurate and efficient technique to carry out large two-dimensional N-body simulations in cosmology. This hybrid code combines the 2d Barnes and Hut Tree method and the 2d Particle-Mesh method. We describe the splitting of force between the PM and the Tree parts. We also estimate error in force for a realistic configuration. Finally, we discuss some tests of the code.Comment: 12 pages, 3 figures, uses jaa.sty. To be submitted to JA

Solar Wakes of Dark Matter Flows

We analyze the effect of the Sun's gravitational field on a flow of cold dark matter (CDM) through the solar system in the limit where the velocity dispersion of the flow vanishes. The exact density and velocity distributions are derived in the case where the Sun is a point mass. The results are extended to the more realistic case where the Sun has a finite size spherically symmetric mass distribution. We find that regions of infinite density, called caustics, appear. One such region is a line caustic on the axis of symmetry, downstream from the Sun, where the flow trajectories cross. Another is a cone-shaped caustic surface near the trajectories of maximum scattering angle. The trajectories forming the conical caustic pass through the Sun's interior and probe the solar mass distribution, raising the possibility that the solar mass distribution may some day be measured by a dark matter detector on Earth. We generalize our results to the case of flows with continuous velocity distributions, such as that predicted by the isothermal model of the Milky Way halo.Comment: 30 pages, 8 figure

A potential WIMP signature for the caustic ring halo model

Weakly Interacting Massive Particle (WIMP) direct detection event rate calculations usually rely on fairly simple, essentially static, analytic halo models. This is largely since the resolution of numerical simulations is not yet large enough to allow the full numerical calculation of the WIMP density and velocity distribution. In this paper we study the direct detection rate, in particular its energy dependence and annual modulation, for the caustic ring halo model. In this model, which uses simple assumptions to model the infall of dark matter onto the halo, the distribution of the cold dark matter particles at the Earth's location has a series of peaks in velocity space. We find that the sign of the annual modulation in the event rate changes as a function of recoil energy. These effects provide a potentially distinctive experimental signal.Comment: 6 pages, 3 figures. Version to appear in Phys. Rev. D. Comparsion with DAMA annual modulation data replaced with qualitative discussio

Functional recombinant protein is present in the pre-induction phases of Pichia pastoris cultures when grown in bioreactors, but not shake-flasks

Background - Pichia pastoris is a widely-used host for recombinant protein production; expression is typically driven by methanol-inducible alcohol oxidase (AOX) promoters. Recently this system has become an important source of recombinant G protein-coupled receptors (GPCRs) for structural biology and drug discovery. The influence of diverse culture parameters (such as pH, dissolved oxygen concentration, medium composition, antifoam concentration and culture temperature) on productivity has been investigated for a wide range of recombinant proteins in P. pastoris. In contrast, the impact of the pre-induction phases on yield has not been as closely studied. In this study, we examined the pre-induction phases of P. pastoris bioreactor cultivations producing three different recombinant proteins: the GPCR, human A2a adenosine receptor (hA2aR), green fluorescent protein (GFP) and human calcitonin gene-related peptide receptor component protein (as a GFP fusion protein; hCGRP-RCP-GFP). Results - Functional hA2aR was detected in the pre-induction phases of a 1 L bioreactor cultivation of glycerol-grown P. pastoris. In a separate experiment, a glycerol-grown P. pastoris strain secreted soluble GFP prior to methanol addition. When glucose, which has been shown to repress AOX expression, was the pre-induction carbon source, hA2aR and GFP were still produced in the pre-induction phases. Both hA2aR and GFP were also produced in methanol-free cultivations; functional protein yields were maintained or increased after depletion of the carbon source. Analysis of the pre-induction phases of 10 L pilot scale cultivations also demonstrated that pre-induction yields were at least maintained after methanol induction, even in the presence of cytotoxic concentrations of methanol. Additional bioreactor data for hCGRP-RCP-GFP and shake-flask data for GFP, horseradish peroxidase (HRP), the human tetraspanins hCD81 and CD82, and the tight-junction protein human claudin-1, demonstrated that bioreactor but not shake flask cultivations exhibit recombinant protein production in the pre-induction phases of P. pastoris cultures. Conclusions - The production of recombinant hA2aR, GFP and hCGRP-RCP-GFP can be detected in bioreactor cultivations prior to methanol induction, while this is not the case for shake-flask cultivations of GFP, HRP, hCD81, hCD82 and human claudin-1. This confirms earlier suggestions of leaky expression from AOX promoters, which we report here for both glycerol- and glucose-grown cells in bioreactor cultivations. These findings suggest that the productivity of AOX-dependent bioprocesses is not solely dependent on induction by methanol. We conclude that in order to maximize total yields, pre-induction phase cultivation conditions should be optimized, and that increased specific productivity may result in decreased biomass yields

A method for detergent-free isolation of membrane proteins in their local lipid environment.

Despite the great importance of membrane proteins, structural and functional studies of these proteins present major challenges. A significant hurdle is the extraction of the functional protein from its natural lipid membrane. Traditionally achieved with detergents, purification procedures can be costly and time consuming. A critical flaw with detergent approaches is the removal of the protein from the native lipid environment required to maintain functionally stable protein. This protocol describes the preparation of styrene maleic acid (SMA) co-polymer to extract membrane proteins from prokaryotic and eukaryotic expression systems. Successful isolation of membrane proteins into SMA lipid particles (SMALPs) allows the proteins to remain with native lipid, surrounded by SMA. We detail procedures for obtaining 25 g of SMA (4 d); explain the preparation of protein-containing SMALPs using membranes isolated from Escherichia coli (2 d) and control protein-free SMALPS using E. coli polar lipid extract (1-2 h); investigate SMALP protein purity by SDS-PAGE analysis and estimate protein concentration (4 h); and detail biophysical methods such as circular dichroism (CD) spectroscopy and sedimentation velocity analytical ultracentrifugation (svAUC) to undertake initial structural studies to characterize SMALPs (∼2 d). Together, these methods provide a practical tool kit for those wanting to use SMALPs to study membrane proteins

Transcriptome Analysis of the Desert Locust Central Nervous System: Production and Annotation of a Schistocerca gregaria EST Database

) displays a fascinating type of phenotypic plasticity, designated as ‘phase polyphenism’. Depending on environmental conditions, one genome can be translated into two highly divergent phenotypes, termed the solitarious and gregarious (swarming) phase. Although many of the underlying molecular events remain elusive, the central nervous system (CNS) is expected to play a crucial role in the phase transition process. Locusts have also proven to be interesting model organisms in a physiological and neurobiological research context. However, molecular studies in locusts are hampered by the fact that genome/transcriptome sequence information available for this branch of insects is still limited. EST information is highly complementary to the existing orthopteran transcriptomic data. Since many novel transcripts encode neuronal signaling and signal transduction components, this paper includes an overview of these sequences. Furthermore, several transcripts being differentially represented in solitarious and gregarious locusts were retrieved from this EST database. The findings highlight the involvement of the CNS in the phase transition process and indicate that this novel annotated database may also add to the emerging knowledge of concomitant neuronal signaling and neuroplasticity events. EST data constitute an important new source of information that will be instrumental in further unraveling the molecular principles of phase polyphenism, in further establishing locusts as valuable research model organisms and in molecular evolutionary and comparative entomology