Frobenius theorem and invariants for Hamiltonian systems

We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assurately restricted to a two-dimensional foliation. In some cases, Frobenius theorem allows the explicit construction of an associated invariant. It is proven the inverse result that, if an invariant is known, then it always can be furnished by Frobenius theorem

On the linearization of the generalized Ermakov systems

A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into this category but others, more generic, systems are also included

Generalized Hamiltonian structures for Ermakov systems

We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations of motion is possible

The ionization structure of the Orion nebula: Infrared line observations and models

Observations of the (O III) 52 and 88 micron lines and the (N III) 57 micron line have been made at 6 positions and the (Ne III) 36 micron line at 4 positions in the Orion Nebula to probe its ionization structure. The measurements, made with a -40" diameter beam, were spaced every 45" in a line south from and including the Trapezium. The wavelength of the (Ne III) line was measured to be 36.013 + or - 0.004 micron. Electron densities and abundance ratios of N(++)/O(++) have been calculated and compared to other radio and optical observations. Detailed one component and two component (bar plus halo) spherical models were calculated for exciting stars with effective temperatures of 37 to 40,000K and log g = 4.0 and 4.5. Both the new infrared observations and the visible line measurements of oxygen and nitrogen require T sub eff approx less than 37,000K. However, the double ionized neon requires a model with T sub eff more than or equal to 39,000K, which is more consistent with that inferred from the radio flux or spectral type. These differences in T sub eff are not due to effects of dust on the stellar radiation field, but are probably due to inaccuracies in the assumed stellar spectrum. The observed N(++)/O(++) ratio is almost twice the N(+)/O(+) ratio. The best fit models give N/H = 8.4 x 10 to the -5 power, O/H = 4.0 x 10 to the -4 power, and Ne/H = 1.3 x 10 to the -4 power. Thus neon and nitrogen are approximately solar, but oxygen is half solar in abundance. From the infrared O(++) lines it is concluded that the ionization bar results from an increase in column depth rather than from a local density enhancement

Eclipsing high-mass binaries I. Light curves and system parameters for CPD-518946, PISMIS24-1 and HD319702

We present first results of a comprehensive photometric O-star survey performed with a robotic twin refractor at the Universit\"atssternwarte Bochum located near Cerro Armazones in Chile. For three high-mass stars, namely Pismis24-1, CPD-518946 and HD319702, we determined the period through the Lafler-Kinman algorithm and model the light curves within the framework of the Roche geometry. For Pismis24-1, a previously known eclipsing binary, we provide first light curves and determined a photometric period of 2.36 days together with an orbital inclination of 61.8 degrees. The best-fitting model solution to the light curves suggest a detached configuration. With a primary temperature of T1 = 42520K we obtain the temperature of the secondary component as T2 = 41500K. CPD-518946 is another known eclipsing binary for which we present a revised photometric period of 1.96 days with an orbital inclination of 58.4 degrees. The system has likely a semi-detached configuration and a mass ratio q = M1/M2 = 2.8. If we adopt a primary temperature of T1 = 34550K we obtain T2 = 21500K for the secondary component. HD319702 is a newly discovered eclipsing binary member of the young open cluster NGC6334. The system shows well-defined eclipses favouring a detached configuration with a period of 2.0 days and an orbital inclination of 67.5 degrees. Combining our photometric result with the primary spectral type O8 III(f) (T1 = 34000K) we derive a temperature of T2 = 25200K for the secondary component.Comment: 7 pages, 4 figures, accepted for publication in Astronomy and Astrophysic

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries

Neutrino-driven Turbulent Convection and Standing Accretion Shock Instability in Three-Dimensional Core-Collapse Supernovae

We conduct a series of numerical experiments into the nature of three-dimensional (3D) hydrodynamics in the postbounce stalled-shock phase of core-collapse supernovae using 3D general-relativistic hydrodynamic simulations of a $27$-$M_\odot$ progenitor star with a neutrino leakage/heating scheme. We vary the strength of neutrino heating and find three cases of 3D dynamics: (1) neutrino-driven convection, (2) initially neutrino-driven convection and subsequent development of the standing accretion shock instability (SASI), (3) SASI dominated evolution. This confirms previous 3D results of Hanke et al. 2013, ApJ 770, 66 and Couch & Connor 2014, ApJ 785, 123. We carry out simulations with resolutions differing by up to a factor of $\sim$4 and demonstrate that low resolution is artificially favorable for explosion in the 3D convection-dominated case, since it decreases the efficiency of energy transport to small scales. Low resolution results in higher radial convective fluxes of energy and enthalpy, more fully buoyant mass, and stronger neutrino heating. In the SASI-dominated case, lower resolution damps SASI oscillations. In the convection-dominated case, a quasi-stationary angular kinetic energy spectrum $E(\ell)$ develops in the heating layer. Like other 3D studies, we find $E(\ell) \propto \ell^{-1}$ in the "inertial range," while theory and local simulations argue for $E(\ell) \propto \ell^{-5/3}$. We argue that current 3D simulations do not resolve the inertial range of turbulence and are affected by numerical viscosity up to the energy containing scale, creating a "bottleneck" that prevents an efficient turbulent cascade.Comment: 24 pages, 15 figures. Accepted for publication in The Astrophysical Journal. Added one figure and made minor modifications to text according to suggestions from the refere

Dust reverberation-mapping of the Seyfert 1 galaxy WPVS48

Using robotic telescopes of the Universitatssternwarte Bochum near Cerro Armazones in Chile, we monitored the z=0.0377 Seyfert 1 galaxy WPVS48 (2MASX J09594263-3112581) in the optical (B and R) and near-infrared (NIR, J and Ks) with a cadence of two days. The light curves show unprecedented variability details. The NIR variation features of WPVS48 are consistent with the corresponding optical variations, but the features appear sharper in the NIR than in the optical, suggesting that the optical photons undergo multiple scatterings. The J and Ks emission, tracing the hot (1600 K) dust echo, lags the B and R variations by on average 64 +/- 4 days and 71 +/- 5 days, respectively (restframe). WPVS48 lies on the known tau-M_V relationship. However, the observed lag is about three times shorter than expected from the dust sublimation radius r_sub inferred from the optical-UV luminosity, and explanations for this common discrepancy are searched for. The sharp NIR echos argue for a face-on torus geometry and allow us to put forward two potential scenarios: 1) as previously proposed, in the equatorial plane of the accretion disk the inner region of the torus is flattened and may come closer to the accretion disk. 2) The dust torus with inner radius r_sub is geometrically and optically thick, so that the observer only sees the facing rim of the torus wall, which lies closer to the observer than the torus equatorial plane and therefore leads to an observed foreshortened lag. Both scenarios are able to explain the factor three discrepancy between tau and r_sub. Longer-wavelength dust reverberation data might enable one to distinguish between the scenarios.Comment: 4 pages, 6 figures, Published in Astronomy and Astrophysic