The Tilt of the Local Velocity Ellipsoid as Seen by Gaia

The Gaia Radial Velocity Spectrometer (RVS) provides a sample of 7,224,631 stars with full six-dimensional phase space information. Bayesian distances of these stars are available from the catalogue of Sch\"onrich et al. (2019). 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 normalising 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 center 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.Comment: MNRAS, revised version contains additional checks on the integrity of the distance

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

A lower limit on the dark particle mass from dSphs

We use dwarf spheroidal galaxies as a tool to attempt to put precise lower limits on the mass of the dark matter particle, assuming it is a sterile neutrino. We begin by making cored dark halo fits to the line of sight velocity dispersions as a function of projected radius (taken from Walker et al. 2007) for six of the Milky Way's dwarf spheroidal galaxies. We test Osipkov-Merritt velocity anisotropy profiles, but find that no benefit is gained over constant velocity anisotropy. In contrast to previous attempts, we do not assume any relation between the stellar velocity dispersions and the dark matter ones, but instead we solve directly for the sterile neutrino velocity dispersion at all radii by using the equation of state for a partially degenerate neutrino gas (which ensures hydrostatic equilibrium of the sterile neutrino halo). This yields a 1:1 relation between the sterile neutrino density and velocity dispersion, and therefore gives us an accurate estimate of the Tremaine-Gunn limit at all radii. By varying the sterile neutrino particle mass, we locate the minimum mass for all six dwarf spheroidals such that the Tremaine-Gunn limit is not exceeded at any radius (in particular at the centre). We find sizeable differences between the ranges of feasible sterile neutrino particle mass for each dwarf, but interestingly there exists a small range 270-280eV which is consistent with all dSphs at the 1-$\sigma$ level.Comment: 13 pages, 2 figures, 1 tabl

Resummation of double logarithms in electroweak high energy processes

At future linear $e^+e^-$ collider experiments in the TeV range, Sudakov double logarithms originating from massive boson exchange can lead to significant corrections to the cross sections of the observable processes. These effects are important for the high precision objectives of the Next Linear Collider. We use the infrared evolution equation, based on a gauge invariant dispersive method, to obtain double logarithmic asymptotics of scattering amplitudes and discuss how it can be applied, in the case of broken gauge symmetry, to the Standard Model of electroweak processes. We discuss the double logarithmic effects to both non-radiative processes and to processes accompanied by soft gauge boson emission. In all cases the Sudakov double logarithms are found to exponentiate. We also discuss double logarithmic effects of a non-Sudakov type which appear in Regge-like processes.Comment: 26 pages, 3 figures, Latex2