Contribution of Gaia Sausage to the Galactic Stellar Halo Revealed by K Giants and Blue Horizontal Branch Stars from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, Sloan Digital Sky Survey, and Gaia

We explore the contribution of the Gaia Sausage to the stellar halo of the Milky Way by making use of a Gaussian mixture model (GMM) and applying it to halo star samples of Large Sky Area Multi-Object Fiber Spectroscopic Telescope K giants, Sloan Extension for Galactic Understanding and Exploration K giants, and Sloan Digital Sky Survey blue horizontal branch stars. The GMM divides the stellar halo into two parts, of which one represents a more metal-rich and highly radially biased component associated with an ancient, head-on collision referred to as the Gaia Sausage, and the other one is a more metal-poor and isotropic halo. A symmetric bimodal Gaussian is used to describe the distribution of spherical velocity of the Gaia Sausage, and we find that the mean absolute radial velocity of the two lobes decreases with the Galactocentric radius. We find that the Gaia Sausage contributes about 41%–74% of the inner (Galactocentric radius r gc < 30 kpc) stellar halo. The fraction of stars of the Gaia Sausage starts to decline beyond r gc ∼ 25–30 kpc, and the outer halo is found to be significantly less influenced by the Gaia Sausage than the inner halo. After the removal of halo substructures found by integrals of motion, the contribution of the Gaia Sausage falls slightly within r gc ∼ 25 kpc but is still as high as 30%–63%. Finally, we select several possible Sausage-related substructures consisting of stars on highly eccentric orbits. The GMM/Sausage component agrees well with the selected substructure stars in their chemodynamical properties, which increases our confidence in the reliability of the GMM fits.

On conjugate difference schemes: the midpoint scheme and the trapezoidal scheme

The preservation of quadratic integrals on approximate solutions of autonomous systems of ordinary differential equations x=f(x), found by the trapezoidal scheme, is investigated. For this purpose, a relation has been established between the trapezoidal scheme and the midpoint scheme, which preserves all quadratic integrals of motion by virtue of Coopers theorem. This relation allows considering the trapezoidal scheme as dual to the midpoint scheme and to find a dual analogue for Coopers theorem by analogy with the duality principle in projective geometry. It is proved that on the approximate solution found by the trapezoidal scheme, not the quadratic integral itself is preserved, but a more complicated expression, which turns into an integral in the limit as t0.Thus the concept of conjugate difference schemes is investigated in pure algebraic way. The results are illustrated by examples of linear and elliptic oscillators. In both cases, expressions preserved by the trapezoidal scheme are presented explicitly.

On the Quadratization of the Integrals for the Many-Body Problem

A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed herein. We introduced additional variables, namely distances and reciprocal distances between bodies, and wrote down a system of differential equations with respect to the coordinates, velocities, and the additional variables. In this case, the system lost its Hamiltonian form, but all the classical integrals of motion of the many-body problem under consideration, as well as new integrals describing the relationship between the coordinates of the bodies and the additional variables are described by linear or quadratic polynomials in these new variables. Therefore, any symplectic Runge–Kutta scheme preserves these integrals exactly. The evidence for the proposed approach is given. To illustrate the theory, the results of numerical experiments for the three-body problem on a plane are presented with the choice of initial data corresponding to the motion of the bodies along a figure of eight (choreographic test).

Analytical study of light ray trajectories in Kerr spacetime in the presence of an inhomogeneous anisotropic plasma

We calculate the exact solutions to the equations of motion that govern the light ray trajectories as they travel in a Kerr black hole’s exterior that is considered to be filled with an inhomogeneous and anisotropic plasmic medium. This is approached by characterizing the plasma through conceiving a radial and an angular structure function, which are let to be constant. The description of the motion is carried out by using the Hamilton–Jacobi method, that allows defining two effective potentials, characterizing the evolution of the polar coordinates. The elliptic integrals of motion are then solved analytically, and the evolution of coordinates is expressed in terms of the Mino time. This way, the three-dimensional demonstrations of the light ray trajectories are given respectively.

Generation of new symmetries from explicit symmetry breaking

We study how the explicit symmetry breaking, through a continuous parameter in the Lagrangian, can actually lead to the creation of different types of symmetries. As examples we consider the motion of a relativistic particle in a curved background, where a nonzero mass breaks the symmetry of the conformal algebra of the metric, and the motion in a Bogoslovsky-Finsler space-time, where a Lorentz violation takes place. In the first case, new nonlocal conserved charges emerge in the place of those which were previously generated by the conformal Killing vectors, while in the second, rational in the momenta integrals of motion appear to substitute the linear expressions corresponding to those boosts which fail to be symmetries.

Flow equations for disordered Floquet systems

In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.