The variety generated by order algebras

Every ordered set can be considered as an algebra in a natural way. We investigate the variety generated by order algebras. We prove, among other things, that this variety is not finitely based and, although locally finite, it is not contained in any finitely generated variety; we describe the bottom of the lattice of its subvarieties

Effects of vertical vibration on hopper flows of granular material

The discharge of granular material from a hopper subject to vertical sinusoidal oscillations was investigated using experiments and discrete element computer simulations. With the hopper exit closed, side-wall convection cells are observed, oriented such that particles move up along the inclined walls of the hopper and down at the center line. The convection cells are a result of the granular bed dilation during free fall and the subsequent interaction with the hopper walls. The mass discharge rate for a vibrating hopper scaled by the discharge rate without vibration reaches a maximum value at a dimensionless velocity amplitude just greater than 1. Further increases in the velocity decrease the discharge rate. The decrease occurs due to a decrease in the bulk density of the discharging material when vibration is applied

Analysis of a Hubble Space Telescope Search for Red Dwarfs: Limits on Baryonic Matter in the Galactic Halo

We re-examine a deep {\it Hubble Space Telescope} pencil-beam search for red dwarfs, stars just massive enough to burn Hydrogen. The authors of this search (Bahcall, Flynn, Gould \& Kirhakos 1994) found that red dwarfs make up less than 6\% of the galactic halo. First, we extrapolate this result to include brown dwarfs, stars not quite massive enough to burn hydrogen; we assume a $1/{\cal M}$ mass function. Then the total mass of red dwarfs and brown dwarfs is $\leq$18\% of the halo. This result is consistent with microlensing results assuming a popular halo model. However, using new stellar models and parallax observations of low mass, low metallicity stars, we obtain much tighter bounds on low mass stars. We find the halo red dwarf density to be $<1\%$ of the halo, while our best estimate of this value is 0.14-0.37\%. Thus our estimate of the halo mass density of red dwarfs drops to 16-40 times less than the reported result of Bahcall et al (1994). For a $1/{\cal M}$ mass function, this suggests a total density of red dwarfs and brown dwarfs of $\sim$0.25-0.67\% of the halo, \ie , (0.9-2.5)\times 10^9\msun out to 50 kpc. Such a low result would conflict with microlensing estimates by the \macho\ group (Alcock \etal 1995a,b).Comment: 13 pages, 2 figures. Figure one only available via fax or snail-mail To be published in ApJL. fig. 2 now available in postscript. Some minor changes in dealing with disk forground. Some cosmetic changes. Updated reference

CMB B -mode non-Gaussianity:Optimal bispectrum estimator and Fisher forecasts

Upcoming cosmic microwave background (CMB) data can be used to explore harmonic 3-point functions that involve the B-mode component of the CMB polarization signal. We focus on bispectra describing the non-Gaussian correlation of the B-mode field and the CMB temperature anisotropies (T) and/or E-mode polarization, i.e. , , and . Such bispectra probe violations of the tensor consistency relation: the model-independent behavior of cosmological correlation functions that involve a large-wavelength tensor mode (gravitational wave). An observed violation of the tensor consistency relation would exclude a large number of inflation models. We describe a generalization of the Komatsu-Spergel-Wandelt (KSW) bispectrum estimator that allows statistical inference on this type of primordial non-Gaussianity with data of the CMB temperature and polarization anisotropies. The generalized estimator shares its statistical properties with the existing KSW estimator and retains the favorable numerical scaling with angular resolution. In this paper we derive the estimator and present a set of Fisher forecasts. We show how the forecasts scale with various experimental parameters such as lower and upper angular band-limit, relevant for e.g. the upcoming ground-based Simons Observatory experiment and proposed LiteBIRD satellite experiment. We comment on possible contaminants due to secondary cosmological and astrophysical sources.Comment: 40 pages, 7 figure

Digging for Dark Matter: Spectral Analysis and Discovery Potential of Paleo-Detectors

Paleo-detectors are a recently proposed method for the direct detection of Dark Matter (DM). In such detectors, one would search for the persistent damage features left by DM--nucleus interactions in ancient minerals. Initial sensitivity projections have shown that paleo-detectors could probe much of the remaining Weakly Interacting Massive Particle (WIMP) parameter space. In this paper, we improve upon the cut-and-count approach previously used to estimate the sensitivity by performing a full spectral analysis of the background- and DM-induced signal spectra. We consider two scenarios for the systematic errors on the background spectra: i) systematic errors on the normalization only, and ii) systematic errors on the shape of the backgrounds. We find that the projected sensitivity is rather robust to imperfect knowledge of the backgrounds. Finally, we study how well the parameters of the true WIMP model could be reconstructed in the hypothetical case of a WIMP discovery.Comment: 14 pages, 5 figures, code available at https://github.com/tedwards2412/paleo_detectors/ . v2: Added additional analysis theory details, matches version published in PR

Dark Matter Capture in the First Stars: a Power Source and Limit on Stellar Mass

The annihilation of weakly interacting massive particles can provide an important heat source for the first (Pop. III) stars, potentially leading to a new phase of stellar evolution known as a "Dark Star". When dark matter (DM) capture via scattering off of baryons is included, the luminosity from DM annihilation may dominate over the luminosity due to fusion, depending on the DM density and scattering cross-section. The influx of DM due to capture may thus prolong the lifetime of the Dark Stars. Comparison of DM luminosity with the Eddington luminosity for the star may constrain the stellar mass of zero metallicity stars; in this case DM will uniquely determine the mass of the first stars. Alternatively, if sufficiently massive Pop. III stars are found, they might be used to bound dark matter properties.Comment: 19 pages, 4 figures, 3 Tables updated captions and graphs, corrected grammer, and added citations revised for submission to JCA

New Models for a Triaxial Milky Way Spheroid and Effect on the Microlensing Optical Depth to the Large Magellanic Cloud

We obtain models for a triaxial Milky Way spheroid based on data by Newberg and Yanny. The best fits to the data occur for a spheroid center that is shifted by 3kpc from the Galactic Center. We investigate effects of the triaxiality on the microlensing optical depth to the Large Magellanic Cloud (LMC). The optical depth can be used to ascertain the number of Massive Compact Halo Objects (MACHOs); a larger spheroid contribution would imply fewer Halo MACHOs. On the one hand, the triaxiality gives rise to more spheroid mass along the line of sight between us and the LMC and thus a larger optical depth. However, shifting the spheroid center leads to an effect that goes in the other direction: the best fit to the spheroid center is_away_ from the line of sight to the LMC. As a consequence, these two effects tend to cancel so that the change in optical depth due to the Newberg/Yanny triaxial halo is at most 50%. After subtracting the spheroid contribution in the four models we consider, the MACHO contribution (central value) to the mass of the Galactic Halo varies from \~(8-20)% if all excess lensing events observed by the MACHO collaboration are assumed to be due to MACHOs. Here the maximum is due to the original MACHO collaboration results and the minimum is consistent with 0% at the 1 sigma error level in the data.Comment: 26 pages, 2 figures. v2: minor revisions. v3: expanded discussion of the local spheroid density and minor revisions to match version published in Journal of Cosmology and Astroparticle Physics (JCAP

Model-Independent Comparison of Direct vs. Indirect Detection of Supersymmetric Dark Matter

We compare the rate for elastic scattering of neutralinos from various nuclei with the flux of upward muons induced by energetic neutrinos from neutralino annihilation in the Sun and Earth. We consider both scalar and axial-vector interactions of neutralinos with nuclei. We find that the event rate in a kg of germanium is roughly equivalent to that in a $10^5$- to $10^7$-m$^2$ muon detector for a neutralino with primarily scalar coupling to nuclei. For an axially coupled neutralino, the event rate in a 50-gram hydrogen detector is roughly the same as that in a 10- to 500-m$^2$ muon detector. Expected experimental backgrounds favor forthcoming elastic-scattering detectors for scalar couplings while the neutrino detectors have the advantage for axial-vector couplings.Comment: 10 pages, self-unpacking uuencoded PostScript fil

Dark Stars and Boosted Dark Matter Annihilation Rates

Dark Stars (DS) may constitute the first phase of stellar evolution, powered by dark matter (DM) annihilation. We will investigate here the properties of DS assuming the DM particle has the required properties to explain the excess positron and elec- tron signals in the cosmic rays detected by the PAMELA and FERMI satellites. Any possible DM interpretation of these signals requires exotic DM candidates, with an- nihilation cross sections a few orders of magnitude higher than the canonical value required for correct thermal relic abundance for Weakly Interacting Dark Matter can- didates; additionally in most models the annihilation must be preferentially to lep- tons. Secondly, we study the dependence of DS properties on the concentration pa- rameter of the initial DM density profile of the halos where the first stars are formed. We restrict our study to the DM in the star due to simple (vs. extended) adiabatic contraction and minimal (vs. extended) capture; this simple study is sufficient to illustrate dependence on the cross section and concentration parameter. Our basic results are that the final stellar properties, once the star enters the main sequence, are always roughly the same, regardless of the value of boosted annihilation or concentration parameter in the range between c=2 and c=5: stellar mass ~ 1000M\odot, luminosity ~ 10^7 L\odot, lifetime ~ 10^6 yrs (for the minimal DM models considered here; additional DM would lead to more massive dark stars). However, the lifetime, final mass, and final luminosity of the DS show some dependence on boost factor and concentration parameter as discussed in the paper.Comment: 37 pages, 11 figure

Calculation of Particle Production by Nambu Goldstone Bosons with Application to Inflation Reheating and Baryogenesis

A semiclassical calculation of particle production by a scalar field in a potential is performed. We focus on the particular case of production of fermions by a Nambu-Goldstone boson $\theta$. We have derived a (non)local equation of motion for the $\theta$-field with the backreaction of the produced particles taken into account. The equation is solved in some special cases, namely for purely Nambu-Goldstone bosons and for the tilted potential $U(\theta ) \propto m^2 \theta^2$. Enhanced production of bosons due to parametric resonance is investigated; we argue that the resonance probably disappears when the expansion of the universe is included. Application of our work on particle production to reheating and an idea for baryogenesis in inflation are mentioned.Comment: Submitted to Physical Review {\rm D}: October 4, 1994 21 page, UM-AC 94-3