Near-Gaussian distributions for modelling discrete stellar velocity data with heteroskedastic uncertainties

The velocity distributions of stellar tracers in general exhibit weak non-Gaussianity encoding information on the orbital composition of a galaxy and the underlying potential. The standard solution for measuring non-Gaussianity involves constructing a series expansion (e.g. the Gauss–Hermite series) that can produce regions of negative probability density. This is a significant issue for the modelling of discrete data with heteroskedastic uncertainties. Here, we introduce a method to construct positive-definite probability distributions by the convolution of a given kernel with a Gaussian distribution. Further convolutions by observational uncertainties are trivial. The statistics (moments and cumulants) of the resulting distributions are governed by the kernel distribution. Two kernels (uniform and Laplace) offer simple drop-in replacements for a Gauss–Hermite series for negative and positive excess kurtosis distributions with the option of skewness. We demonstrate the power of our method by an application to real and mock line-of-sight velocity data sets on dwarf spheroidal galaxies, where kurtosis is indicative of orbital anisotropy and hence a route to breaking the mass–anisotropy degeneracy for the identification of cusped versus cored dark matter profiles. Data on the Fornax dwarf spheroidal galaxy indicate positive excess kurtosis and hence favour a cored dark matter profile. Although designed for discrete data, the analytic Fourier transforms of the new models also make them appropriate for spectral fitting, which could improve the fits of high-quality data by avoiding unphysical negative wings in the line-of-sight velocity distribution

MASS ESTIMATORS for FLATTENED DISPERSION-SUPPORTED GALAXIES

We investigate the reliability of mass estimators based on the observable velocity dispersion and half-light radius R $_{h}$ for dispersion-supported galaxies. We show how to extend them to flattened systems and provide simple formulae for the mass within an ellipsoid under the assumption the dark-matter density and the stellar density are stratified on the same self-similar ellipsoids. We demonstrate explicitly that the spherical mass estimators give accurate values for the mass within the half-light ellipsoid, provided R $_{h}$ is replaced by its "circularized" analog ${R}_{{\rm{h}}}\sqrt{1-\epsilon }$. We provide a mathematical justification for this surprisingly simple and effective workaround. It means, for example, that the mass-to-light ratios are valid not just when the light and dark matter are spherically distributed, but also when they are flattened on ellipsoids of the same constant shape.This is the final version of the article. It first appeared from the Institute of Physics via https://doi.org/10.3847/2041-8205/830/2/L2

A two-parameter family of double-power-law biorthonormal potential-density expansions

Biorthonormal basis function expansions are widely used in galactic dynamics, both to study problems in galactic stability and to provide numerical algorithms to evolve collisionless stellar systems. They also provide a compact and efficient description of the structure of numerical dark matter haloes in cosmological simulations. We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley, Sanders, Evans & Erkal expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the $\gamma$ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding further examples. In the process, we also uncovered a novel integral transform solution to Poisson's equation

The super-NFW model: An analytic dynamical model for cold dark matter haloes and elliptical galaxies

An analytic galaxy model with $\rho \sim r^{-1}$ at small radii and $\rho \sim r^{-3.5}$ at large radii is presented. The asymptotic density fall-off is slower than the Hernquist model, but faster than the Navarro-Frenk-White (NFW) profile for dark matter haloes, and so in accord with recent evidence from cosmological simulations. The model provides the zeroth-order term in a biorthornomal basis function expansion, meaning that axisymmetric, triaxial and lopsided distortions can easily be added (much like the Hernquist model itself which is the zeroth-order term of the Hernquist-Ostriker expansion). The properties of the spherical model, including analytic distribution functions which are either isotropic, radially anisotropic or tangentially anisotropic, are discussed in some detail. The analogue of the mass-concentration relation for cosmological haloes is provided.EJL and JLS acknowledge financial support from the Science and Technology Facilities Council

Tidal disruption of dwarf spheroidal galaxies: The strange case of Crater II

Dwarf spheroidal galaxies of the Local Group obey a relationship between the line-of-sight velocity dispersion and half-light radius, although there are a number of dwarfs that lie beneath this relation with suppressed velocity dispersion. The most discrepant of these (in the Milky Way) is the ‘feeble giant’ Crater II. Using analytic arguments supported by controlled numerical simulations of tidally stripped flattened two-component dwarf galaxies, we investigate interpretations of Crater II within standard galaxy formation theory. Heavy tidal disruption is necessary to explain the velocity dispersion suppression which is plausible if the proper motion of Crater II is (μα∗, μδ ) = (−0.21 ± 0.09, −0.24 ± 0.09) mas yr−1. Furthermore, we demonstrate that the velocity dispersion of tidally disrupted systems is solely a function of the total mass-loss even for weakly embedded and flattened systems. The half-light radius evolution depends more sensitively on orbital phase and the properties of the dark matter profile. The half-light radius of weakly embedded cusped systems rapidly decreases producing some tension with the Crater II observations. This tension is alleviated by cored dark matter profiles, in which the half-light radius can grow after tidal disruption. The evolution of flattened galaxies is characterized by two competing effects: tidal shocking makes the central regions rounder whilst tidal distortion produces a prolate tidally locked outer envelope. After ∼70 per cent of the central mass is lost, tidal distortion becomes the dominant effect and the shape of the central regions of the galaxy tends to a universal prolate shape irrespective of the initial shape

Higgs Messengers

We explore the consequences of the Higgs fields acting as messengers of supersymmetry breaking. The hidden-sector paradigm in the gauge mediation framework is relaxed by allowing two types of gauge-invariant, renormalizable operators that are typically discarded: direct coupling between the Higgses and supersymmetry breaking singlets, and Higgs-messenger mixing terms. The most important phenomenological consequence is a flavor-dependent shift in sfermion masses. This is from a one-loop contribution, which we compute for a general set of weak doublet messengers. We also study a couple of explicit models in detail, finding that precision electroweak constraints can be satisfied with a spectrum significantly different from that of gauge mediation.Comment: 20 pages, 5 figure

Reconciling actual and perceived rates of predation by domestic cats

This is the final version. Available on open access from Wiley via the DOI in this recordThe predation of wildlife by domestic cats (Felis catus) is a complex problem: Cats are popular companion animals in modern society but are also acknowledged predators of birds, herpetofauna, invertebrates, and small mammals. A comprehensive understanding of this conservation issue demands an understanding of both the ecological consequence of owning a domestic cat and the attitudes of cat owners. Here, we determine whether cat owners are aware of the predatory behavior of their cats, using data collected from 86 cats in two UK villages. We examine whether the amount of prey their cat returns influences the attitudes of 45 cat owners toward the broader issue of domestic cat predation. We also contribute to the wider understanding of physiological, spatial, and behavioral drivers of prey returns among cats. We find an association between actual prey returns and owner predictions at the coarse scale of predatory/nonpredatory behavior, but no correlation between the observed and predicted prey-return rates among predatory cats. Cat owners generally disagreed with the statement that cats are harmful to wildlife, and disfavored all mitigation options apart from neutering. These attitudes were uncorrelated with the predatory behavior of their cats. Cat owners failed to perceive the magnitude of their cats' impacts on wildlife and were not influenced by ecological information. Management options for the mitigation of cat predation appear unlikely to work if they focus on "predation awareness" campaigns or restrictions of cat freedom. We consider both the ecological consequence of owning a domestic cat and the attitudes of cat owners. Our findings suggest cat owners fail to perceive the magnitude of their cats' impacts on wildlife, with no correlation between the observed and predicted prey return rates among predatory cats. On the basis of opinions of cat owners in this study, management options for the mitigation of cat predation appear unlikely to work if they focus on "predation awareness" campaigns, or restrictions of cat freedom.International Fund for Animal WelfareUniversity of ExeterEuropean Social FundNatural Environment Research Council (NERC

Galaxy halo expansions: a new biorthogonal family of potential-density pairs

Efficient expansions of the gravitational field of (dark) haloes have two main uses in the modelling of galaxies: first, they provide a compact representation of numerically-constructed (or real) cosmological haloes, incorporating the effects of triaxiality, lopsidedness or other distortion. Secondly, they provide the basis functions for self-consistent field expansion algorithms used in the evolution of $N$-body systems. We present a new family of biorthogonal potential-density pairs constructed using the Hankel transform of the Laguerre polynomials. The lowest-order density basis functions are double-power-law profiles cusped like $\rho \sim r^{-2 + 1/\alpha}$ at small radii with asymptotic density fall-off like $\rho \sim r^{-3 -1/(2\alpha)}$. Here, $\alpha$ is a parameter satisfying $\alpha \ge 1/2$. The family therefore spans the range of inner density cusps found in numerical simulations, but has much shallower -- and hence more realistic -- outer slopes than the corresponding members of the only previously-known family deduced by Zhao (1996) and exemplified by Hernquist & Ostriker (1992). When $\alpha =1$, the lowest-order density profile has an inner density cusp of $\rho \sim r^{-1}$ and an outer density slope of $\rho \sim r^{-3.5}$, similar to the famous Navarro, Frenk & White (1997) model. For this reason, we demonstrate that our new expansion provides a more accurate representation of flattened NFW haloes than the competing Hernquist-Ostriker expansion. We utilize our new expansion by analysing a suite of numerically-constructed haloes and providing the distributions of the expansion coefficients.JLS and EJL acknowledge the support of the STFC

Indirect dark matter detection for flattened dwarf galaxies

Gamma-ray experiments seeking to detect evidence of dark matter annihilation in dwarf spheroidal galaxies require knowledge of the distribution of dark matter within these systems. We analyze the effects of flattening on the annihilation (J) and decay (D) factors of dwarf spheroidal galaxies with both analytic and numerical methods. Flattening has two consequences: first, there is a geometric effect as the squeezing (or stretching) of the dark matter distribution enhances (or diminishes) the J-factor; second, the line of sight velocity dispersion of stars must hold up the flattened baryonic component in the flattened dark matter halo. We provide analytic formulas and a simple numerical approach to estimate the correction to the J- and D-factors required over simple spherical modeling. The formulas are validated with a series of equilibrium models of flattened stellar distributions embedded in flattened dark-matter distributions. We compute corrections to the J- and D-factors for the Milky Way dwarf spheroidal galaxies under the assumption that they are all prolate or all oblate and find that the hierarchy of J-factors for the dwarf spheroidals is slightly altered (typical correction factors for an ellipticity of 0.4 are 0.75 for the oblate case and 1.6 for the prolate case). We demonstrate that spherical estimates of the D-factors are very insensitive to the flattening and introduce uncertainties significantly less than the uncertainties in the D-factors from the other observables for all the dwarf spheroidals (for example, $^{+10per~cent}_{−3per~cent}$ for a typical ellipticity of 0.4). We conclude by investigating the spread in correction factors produced by triaxial figures and provide uncertainties in the J-factors for the dwarf spheroidals using different physically motivated assumptions for their intrinsic shape and axis alignments. We find that the uncertainty in the J-factors due to triaxiality increases with the observed ellipticity and, in general, introduces uncertainties of a factor of 2 in the J-factors. We discuss our results in light of the reported gamma-ray signal from the highly flattened ultrafaint Reticulum II. Tables of the J- and D-factors for the Milky Way dwarf spheroidal galaxies are provided (assuming an oblate or prolate structure) along with a table of the uncertainty on these factors arising from the unknown triaxiality.Science and Technology Facilities CouncilThis is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevD.94.06352

Cognitive control in belief-laden reasoning during conclusion processing: An ERP study

Belief bias is the tendency to accept conclusions that are compatible with existing beliefs more frequently than those that contradict beliefs. It is one of the most replicated behavioral findings in the reasoning literature. Recently, neuroimaging studies using functional magnetic resonance imaging (fMRI) and event-related potentials (ERPs) have provided a new perspective and have demonstrated neural correlates of belief bias that have been viewed as supportive of dual-process theories of belief bias. However, fMRI studies have tended to focus on conclusion processing, while ERPs studies have been concerned with the processing of premises. In the present research, the electrophysiological correlates of cognitive control were studied among 12 subjects using high-density ERPs. The analysis was focused on the conclusion presentation phase and was limited to normatively sanctioned responses to valid–believable and valid–unbelievable problems. Results showed that when participants gave normatively sanctioned responses to problems where belief and logic conflicted, a more positive ERP deflection was elicited than for normatively sanctioned responses to nonconflict problems. This was observed from −400 to −200 ms prior to the correct response being given. The positive component is argued to be analogous to the late positive component (LPC) involved in cognitive control processes. This is consistent with the inhibition of empirically anomalous information when conclusions are unbelievable. These data are important in elucidating the neural correlates of belief bias by providing evidence for electrophysiological correlates of conflict resolution during conclusion processing. Moreover, they are supportive of dual-process theories of belief bias that propose conflict detection and resolution processes as central to the explanation of belief bias