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

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

Skinny Milky Way please, says Sagittarius

Motivated by recent observations of the Sagittarius stream, we devise a rapid algorithm to generate faithful representations of the centroids of stellar tidal streams formed in a disruption of a progenitor of an arbitrary mass in an arbitrary potential. Our method works by releasing swarms of test particles at the Lagrange points around the satellite and subsequently evolving them in a combined potential of the host and the progenitor. We stress that the action of the progenitor's gravity is crucial to making streams that look almost indistinguishable from the N-body realizations, as indeed ours do. The method is tested on mock stream data in three different Milky Way potentials with increasing complexity, and is shown to deliver unbiased inference on the Galactic mass distribution out to large radii. When applied to the observations of the Sagittarius stream, our model gives a natural explanation of the stream's apocentric distances and the differential orbital precession. We, therefore, provide a new independent measurement of the Galactic mass distribution beyond 50 kpc. The Sagittarius stream model favours a light Milky Way with the mass 4.1 +/- 0.4 x 10^11 M_sun at 100 kpc, which can be extrapolated to 5.6 +/- 1.2 x 10^11 M_sun at 200 kpc. Such a low mass for the Milky Way Galaxy is in good agreement with estimates from the kinematics of halo stars and from the satellite galaxies (once Leo I is removed from the sample). It entirely removes the "Too Big To Fail Problem".RCUK, OtherThis is the author accepted manuscript. The final version is available from Oxford University Press via http://dx.doi.org/10.1093/mnras/stu198

Hamiltonians of spherical Galaxies in action-angle coordinates

We present a simple formula for the Hamiltonian in terms of the actions for spherically symmetric, scale-free potentials. The Hamiltonian is a power-law or logarithmic function of a linear combination of the actions. Our expression reduces to the well-known results for the familiar cases of the harmonic oscillator and the Kepler potential. For other power-laws, as well as for the singular isothermal sphere, it is exact for the radial and circular orbits, and very accurate for general orbits. Numerical tests show that the errors are always small, with mean errors across a grid of actions always less than 1 % and maximum errors less than 2.5 %. Simple first-order corrections can reduce mean errors to less than 0.6 % and maximum errors to less than 1 %. We use our new result to show that :[1] the misalignment angle between debris in a stream and a progenitor is always very nearly zero in spherical scale-free potentials, demonstrating that streams can be sometimes well approximated by orbits, [2] the effects of an adiabatic change in the stellar density profile in the inner regions of a galaxy weaken any existing 1/r density cusp, which is reduced to $1/r^{1/3}$. More generally, we derive the full range of adiabatic cusp transformations and show how to relate the starting cusp index to the final cusp index. It follows that adiabatic transformations can never erase a dark matter cusp.AW and AB acknowledge the support of STFC

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

Dogs that Don't Bark (The Tale of Baryonic Dark Matter in Galaxies)

Fifteen years or so ago, it was commonly argued; ``If we want to believe the observations rather than our prejudice, we should take as our best bet that dark haloes are baryonic.'' Such a viewpoint is not often heard today. This change-of-mind has been enforced upon us largely by the microlensing experiments. Particle dark matter differs from (most types of) baryonic dark matter in that it does not produce microlensing events. The familiar parade of baryonic candidates has now been whittled down, and perhaps only one remains as a possible substantial contributor to the dark matter in the Galaxy's halo. This review assesses the distribution of missing matter in the Galaxy, the likely baryonic dark matter suspects, the evidence from microlensing and from the halo white dwarf searches

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