Predicting species abundance distributions by simultaneously using number and biomass as units of measurement

The universal observation that some species in an ecological community are common, but many more are rare, is neatly encapsulated in a species abundance distribution (SAD)1. However, the shape of the distribution can depend on the currency used to measure abundance 2. Here we show how the SADs for numerical abundance and biomass are related and how this relationship can be used to predict the form of the SAD. When plotted in log numerical abundance, log biomass space, species points lie within an approximately triangular area the limits of which are set by body size range, and the upper limit of abundance in both metrics. Under the simplifying, but reasonable, assumption that the observed scatter of species within this region is random, the shape of the SAD is immediately derived from simple geometrical considerations. For the SAD of numerical abundance this is a power curve. The biomass SAD can be either a power curve or, more frequently, a unimodal curve, which can approximate a log normal. This log triangular random placement model serves as a null hypothesis against which actual communities can be compared. Data from two intensively surveyed local communities indicate that it can give a good approximation, with species scattered within a triangle. Further, we can predict the consequences, for the SAD, of size-selective sampling protocols. We argue that mechanistic models of SADs must be able to account for the relative abundance of species in alternative currencies. Moreover, this approach will shed light on niche packing and may have application in environmental monitoring

Theoretical Clues to the Ultraviolet Diversity of Type Ia Supernovae

The effect of metallicity on the observed light of Type Ia supernovae (SNe Ia) could lead to systematic errors as the absolute magnitudes of local and distant SNe Ia are compared to measure luminosity distances and determine cosmological parameters. The UV light may be especially sensitive to metallicity, though different modeling methods disagree as to the magnitude, wavelength dependence, and even the sign of the effect. The outer density structure, ^56 Ni, and to a lesser degree asphericity, also impact the UV. We compute synthetic photometry of various metallicity-dependent models and compare to UV/optical photometry from the Swift Ultra-Violet/Optical Telescope. We find that the scatter in the mid-UV to near-UV colors is larger than predicted by changes in metallicity alone and is not consistent with reddening. We demonstrate that a recently employed method to determine relative abundances using UV spectra can be done using UVOT photometry, but we warn that accurate results require an accurate model of the cause of the variations. The abundance of UV photometry now available should provide constraints on models that typically rely on UV spectroscopy for constraining metallicity, density, and other parameters. Nevertheless, UV spectroscopy for a variety of SN explosions is still needed to guide the creation of accurate models. A better understanding of the influences affecting the UV is important for using SNe Ia as cosmological probes, as the UV light may test whether SNe Ia are significantly affected by evolutionary effects.Comment: 10 pages. Submitted to Ap

Synthetic Spectra of Hydrodynamic Models of Type Ia Supernovae

We present detailed NLTE synthetic spectra of hydrodynamic SNe Ia models. We make no assumptions about the form of the spectrum at the inner boundary. We calculate both Chandrasekhar-mass deflagration models and sub-Chandrasekhar ``helium detonators.'' Gamma-ray deposition is handled in a simple, accurate manner. We have parameterized the storage of energy that arises from the time dependent deposition of radioactive decay energy in a reasonable manner, that spans the expected range. We find that the Chandrasekhar-mass deflagration model W7 of Nomoto etal shows good agreement with the observed spectra of SN 1992A and SN 1994D, particularly in the UV, where our models are expected to be most accurate. The sub-Chandrasekhar models do not reproduce the UV deficit observed in normal SNe Ia. They do bear some resemblance to sub-luminous SNe Ia, but the shape of the spectra (i.e. the colors) are opposite to that of the observed ones and the intermediate mass element lines such as Si II, and Ca II are extremely weak, which seems to be a generic difficulty of the models. Although the sub-Chandrasekhar models have a significant helium abundance (unlike Chandrasekhar-mass models), helium lines are not prominent in the spectra near maximum light and thus do not act as a spectral signature for the progenitor.Comment: submitted to ApJ, 26 pages, 10 figures, uses LaTeX styles aasms4.sty and natbib.sty Also available at: http://www.nhn.ou.edu/~baron

Total reaction cross sections from 141^{141}141Pr(α\alpha,α\alpha)141^{141}Pr elastic scattering and α\alpha-induced reaction cross sections at low energies

Elastic scattering data for $^{141}$Pr($\alpha$,$\alpha$)$^{141}$Pr have been analyzed to derive a new energy-dependent local potential for the $^{141}$Pr-$\alpha$ system. This potential is used successfully to predict the cross section of the $^{141}$Pr($\alpha$,n)$^{144}$Pm reaction at low energies where new experimental data have become available very recently. Contrary to various global potentials, this new potential is able to reproduce simultaneously elastic scattering data around and above the Coulomb barrier and reaction data below the Coulomb barrier for the $^{141}$Pr-$\alpha$ system. Reasons for the partial failure of the global potentials are explained by intrinsic properties of the scattering matrix and their variation with energy. The new local potential may become the basis for the construction of a new global $\alpha$-nucleus potential.Comment: 12 pages, 8 figures, Phys. Rev. C, accepte

Testing isomorphism of graded algebras

We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that often dramatically improve the performance of the algorithm and report on an implementation in Magma

Rates and Properties of Strongly Gravitationally Lensed Supernovae and their Host Galaxies in Time-Domain Imaging Surveys

Supernovae that are strongly gravitationally lensed (gLSNe) by galaxies are powerful probes of astrophysics and cosmology that will be discovered systematically by next-generation wide-field, high-cadence imaging surveys such as the Zwicky Transient Facility (ZTF) and the Large Synoptic Survey Telescope (LSST). Here we use pixel-level simulations that include dust, observing strategy, and multiple supernova subtypes to forecast the rates and properties of gLSNe that ZTF and LSST will find. Applying the resolution-insensitive discovery strategy of Goldstein et al. (2018), we forecast that ZTF (LSST) can discover 0.02 (0.79) 91bg-like, 0.17 (5.92) 91T-like, 1.22 (47.84) Type Ia, 2.76 (88.51) Type IIP, 0.31 (12.78) Type IIL, and 0.36 (15.43) Type Ib/c gLSNe per year. We also forecast that the surveys can discover at least 3.75 (209.32) Type IIn gLSNe per year, for a total of at least 8.60 (380.60) gLSNe per year under fiducial observing strategies. ZTF gLSNe have a median $z_s=0.9$, $z_l=0.35$, $\mu_\mathrm{tot}=30$, $\Delta t_\mathrm{max}= 10$ days, $\min(\theta)= 0.25^{\prime\prime}$, and $N_\mathrm{img} = 4$. LSST gLSNe are less compact and less magnified, with a median $z_s=1.0$, $z_l=0.4$, $\mu_\mathrm{tot}\approx6$, $\Delta t_\mathrm{max} = 25$ days, $\min(\theta)=0.6^{\prime\prime}$, and $N_\mathrm{img} = 2$. As the properties of lensed host galaxy arcs provide critical information for lens mass modeling, we develop a model of the supernova--host galaxy connection and use it to simulate realistic images of the supernova--host--lens systems. We find that the vast majority of gLSN host galaxies will be multiply imaged, enabling detailed constraints on lens models with sufficiently deep high-resolution imaging taken after the supernova has faded. We release the results of our simulations to the public as catalogs at this URL: http://portal.nersc.gov/project/astro250/glsne/.Comment: 57 pages, 66 equations, 36 figures, 4 tables, Submitted to ApJS, comments welcome, v2 replaced some figures with rasterized versions to reduce load on PDF viewer