A study of rotating globular clusters - the case of the old, metal-poor globular cluster NGC 4372

Aims: We present the first in-depth study of the kinematic properties and derive the structural parameters of NGC 4372 based on the fit of a Plummer profile and a rotating, physical model. We explore the link between internal rotation to different cluster properties and together with similar studies of more GCs, we put these in the context of globular cluster formation and evolution. Methods: We present radial velocities for 131 cluster member stars measured from high-resolution FLAMES/GIRAFFE observations. Their membership to the GC is additionally confirmed from precise metallicity estimates. Using this kinematic data set we build a velocity dispersion profile and a systemic rotation curve. Additionally, we obtain an elliptical number density profile of NGC 4372 based on optical images using a MCMC fitting algorithm. From this we derive the cluster's half-light radius and ellipticity as r_h=3.4'+/-0.04' and e=0.08+/-0.01. Finally, we give a physical interpretation of the observed morphological and kinematic properties of this GC by fitting an axisymmetric, differentially rotating, dynamical model. Results: Our results show that NGC 4372 has an unusually high ratio of rotation amplitude to velocity dispersion (1.2 vs. 4.5 km/s) for its metallicity. This, however, puts it in line with two other exceptional, very metal-poor GCs - M 15 and NGC 4590. We also find a mild flattening of NGC 4372 in the direction of its rotation. Given its old age, this suggests that the flattening is indeed caused by the systemic rotation rather than tidal interactions with the Galaxy. Additionally, we estimate the dynamical mass of the GC M_dyn=2.0+/-0.5 x 10^5 M_Sun based on the dynamical model, which constrains the mass-to-light ratio of NGC 4372 between 1.4 and 2.3 M_Sun/L_Sun, representative of an old, purely stellar population.Comment: Accepted for publication in A&A, 12 pages, 14 figures, 2 table

Mode Transitions in Magnetically Shielded Hall Effect Thrusters

A mode transition study is conducted in magnetically shielded thrusters where the magnetic field magnitude is varied to induce mode transitions. Three different oscillatory modes are identified with the 20-kW NASA-300MS-2 and the 6-kW H6MS: Mode 1) global mode similar to unshielded thrusters at low magnetic fields, Mode 2) cathode oscillations at nominal magnetic fields, and Mode 3) combined spoke, cathode and breathing mode oscillations at high magnetic fields. Mode 1 exhibits large amplitude, low frequency (1-10 kHz), breathing mode type oscillations where discharge current mean value and oscillation amplitude peak. The mean discharge current is minimized while thrust-to-power and anode efficiency are maximized in Mode 2, where higher frequency (50-90 kHz), low amplitude, cathode oscillations dominate. Thrust is maximized in Mode 3 and decreases by 5-6% with decreasing magnetic field strength. The presence or absence of spokes and strong cathode oscillations do not affect each other or discharge current. Similar to unshielded thrusters, mode transitions and plasma oscillations affect magnetically shielded thruster performance and should be characterized during system development

Two-Center Black Holes Duality-Invariants for stu Model and its lower-rank Descendants

We classify 2-center extremal black hole charge configurations through duality-invariant homogeneous polynomials, which are the generalization of the unique invariant quartic polynomial for single-center black holes based on homogeneous symmetric cubic special Kaehler geometries. A crucial role is played by an horizontal SL(p,R) symmetry group, which classifies invariants for p-center black holes. For p = 2, a (spin 2) quintet of quartic invariants emerge. We provide the minimal set of independent invariants for the rank-3 N = 2, d = 4 stu model, and for its lower-rank descendants, namely the rank-2 st^2 and rank-1 t^3 models; these models respectively exhibit seven, six and five independent invariants. We also derive the polynomial relations among these and other duality invariants. In particular, the symplectic product of two charge vectors is not independent from the quartic quintet in the t^3 model, but rather it satisfies a degree-16 relation, corresponding to a quartic equation for the square of the symplectic product itself.Comment: 1+31 pages; v2: amendments in Sec. 9, App. C added, other minor refinements, Refs. added; v3: Ref. added, typos fixed. To appear on J.Math.Phy

Diagonalization of multicomponent wave equations with a Born-Oppenheimer example

A general method to decouple multicomponent linear wave equations is presented. First, the Weyl calculus is used to transform operator relations into relations between c-number valued matrices. Then it is shown that the symbol representing the wave operator can be diagonalized systematically up to arbitrary order in an appropriate expansion parameter. After transforming the symbols back to operators, the original problem is reduced to solving a set of linear uncoupled scalar wave equations. The procedure is exemplified for a particle with a Born-Oppenheimer-type Hamiltonian valid through second order in h. The resulting effective scalar Hamiltonians are seen to contain an additional velocity-dependent potential. This contribution has not been reported in recent studies investigating the adiabatic motion of a neutral particle moving in an inhomogeneous magnetic field. Finally, the relation of the general method to standard quantum-mechanical perturbation theory is discussed