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

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

Magellanic Mayhem: Metallicities and Motions

We assemble a catalogue of Magellanic Cloud red giants from Data Release 2 of the $Gaia$ mission and, utilising machine learning methods, obtain photometric metallicity estimates for them. In doing so, we are able to chemically map the entirety of the Magellanic System at once. Our high resolution maps reveal a plethora of substructure, with the Large Magellanic Cloud (LMC) bar and spiral arm being readily apparent. We uncover a curious spiral-like feature in the southern portion of the LMC disc, hosting relatively metal-rich giants and likely a by-product of historic encounter with the Small Magellanic Cloud (SMC). Modelling the LMC as an inclined thin disc, we find a shallow metallicity gradient of $-0.048 \pm 0.001$ dex/kpc out to $\sim 12^{\circ}$ from the centre of the dwarf. We see evidence that the Small Magellanic Cloud is disrupting, with its outer iso-density contours displaying the S-shape symptomatic of tidal stripping. On studying the proper motions of the SMC giants, we observe a population of them being violently dragged towards the larger Cloud. The perturbed stars predominately lie in front of the SMC, and we interpret that they exist as a tidal tail of the dwarf, trailing in its motion and undergoing severe disruption from the LMC. We find the metallicity structure in the Magellanic Bridge region to be complex, with evidence for a composite nature in this stellar population, consisting of both LMC and SMC debris

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

Microlensing, Brown Dwarfs and GAIA

The GAIA satellite can precisely measure the masses of nearby brown dwarfs and lower main sequence stars by the microlensing effect. The scientific yield is maximised if the microlensing event is also followed with ground-based telescopes to provide densely sampled photometry. There are two possible strategies. First, ongoing events can be triggered by photometric or astrometric alerts by GAIA. Second, events can be predicted using known high proper motion stars as lenses. This is much easier, as the location and time of an event can be forecast. Using the GAIA source density, we estimate that the sample size of high proper motion ($>300$ mas yr$^{-1}$) brown dwarfs needed to provide predictable events during the 5 year mission lifetime is surprisingly small, only of the order of a hundred. This is comparable to the number of high proper motion brown dwarfs already known from the work of the UKIDSS Large Area Survey and the all-sky WISE satellite. Provided the relative parallax of the lens and the angular Einstein radius can be recovered from astrometric data, then the mass of the lens can be found. Microlensing provides the only way of measuring the masses of individual objects irrespective oftheir luminosity. So, microlensing with GAIA is the best way to carry out an inventory of masses in the brown dwarf regime

The tilt of the local velocity ellipsoid as seen by Gaia

The Gaia Radial Velocity Spectrometer (RVS) provides a sample of 7224 631 stars with full six-dimensional phase space information. Bayesian distances of these stars are available from the catalogue of Schönrich, McMillan & Eyer. We exploit this to map out the behaviour of the velocity ellipsoid within 5 kpc of the Sun. We find that the tilt of the disc-dominated RVS sample is accurately described by the relation $\alpha = (0.952 \pm 0.007)\arctan (|z|/R)$, where (R, z) are cylindrical polar coordinates. This corresponds to velocity ellipsoids close to spherical alignment (for which the normalizing constant would be unity) and pointing towards the Galactic Centre. Flattening of the tilt of the velocity ellipsoids is enhanced close to the plane and Galactic Centre, whilst at high elevations far from the Galactic Centre the population is consistent with exact spherical alignment. Using the LAMOST catalogue cross-matched with Gaia DR2, we construct thin disc and halo samples of reasonable purity based on metallicity. We find that the tilt of thin disc stars straddles $\alpha = (0.909{\!-\!}1.038)\arctan (|z|/R)$, and of halo stars straddles $\alpha = (0.927{\!-\!}1.063)\arctan (|z|/R)$. We caution against the use of reciprocal parallax for distances in studies of the tilt, as this can lead to serious artefacts

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