Symmetry, bifurcation and stacking of the central configurations of the planar 1+4 body problem

In this work we are interested in the central configurations of the planar 1+4 body problem where the satellites have different infinitesimal masses and two of them are diametrically opposite in a circle. We can think this problem as a stacked central configuration too. We show that the configuration are necessarily symmetric and the other sattelites has the same mass. Moreover we proved that the number of central configuration in this case is in general one, two or three and in the special case where the satellites diametrically opposite have the same mass we proved that the number of central configuration is one or two saying the exact value of the ratio of the masses that provides this bifurcation.Comment: 9 pages, 2 figures. arXiv admin note: text overlap with arXiv:1103.627

Chaos around a H\'enon-Heiles-inspired exact perturbation of a black hole

A solution of the Einstein's equations that represents the superposition of a Schwarszchild black hole with both quadrupolar and octopolar terms describing a halo is exhibited. We show that this solution, in the Newtonian limit, is an analog to the well known H\'enon-Heiles potential. The integrability of orbits of test particles moving around a black hole representing the galactic center is studied and bounded zones of chaotic behavior are found.Comment: 7 pages Revte

Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics

The recent experimental implementation of condensed matter models in optical lattices has motivated research on their nonequilibrium behavior. Predictions on the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective BCS Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently nonadiabatic ramping scheme is essential to excite the nonequilibrium dynamics, and (ii) overheating beyond the critical temperature of superconductivity must be avoided. For commonly discussed interaction ramps there is no clear separation of the corresponding energy scales. Here we show that the matching of both conditions is simplified by the intrinsic relaxation behavior of ultracold fermionic systems: For the particular example of a linear ramp we examine the transient regime of prethermalization [M. Moeckel and S. Kehrein, Phys. Rev. Lett. 100, 175702 (2008)] under the crossover from sudden to adiabatic switching using Keldysh perturbation theory. A real-time analysis of the momentum distribution exhibits a temporal separation of an early energy relaxation and its later thermalization by scattering events. For long but finite ramping times this separation can be large. In the prethermalization regime the momentum distribution resembles a zero temperature Fermi liquid as the energy inserted by the ramp remains located in high energy modes. Thus ultracold fermions prove robust to heating which simplifies the observation of nonequilibrium BCS dynamics in optical lattices.Comment: 27 pages, 8 figures Second version with small modifications in section

Large normally hyperbolic cylinders in a priori stable Hamiltonian systems

We prove the existence of normally hyperbolic invariant cylinders in nearly integrable hamiltonian systems

Stellar Encounters with Massive Star-Disk Systems

The dense, clustered environment in which massive stars form can lead to interactions with neighboring stars. It has been hypothesized that collisions and mergers may contribute to the growth of the most massive stars. In this paper we extend the study of star-disk interactions to explore encounters between a massive protostar and a less massive cluster sibling using the publicly available SPH code GADGET-2. Collisions do not occur in the parameter space studied, but the end state of many encounters is an eccentric binary with a semi-major axis ~ 100 AU. Disk material is sometimes captured by the impactor. Most encounters result in disruption and destruction of the initial disk, and periodic torquing of the remnant disk. We consider the effect of the changing orientation of the disk on an accretion driven jet, and the evolution of the systems in the presence of on-going accretion from the parent core.Comment: 11 pages, 10 figures, accepted to Ap

Straight Line Orbits in Hamiltonian Flows

We investigate periodic straight-line orbits (SLO) in Hamiltonian force fields using both direct and inverse methods. A general theorem is proven for natural Hamiltonians quadratic in the momenta in arbitrary dimension and specialized to two and three dimension. Next we specialize to homogeneous potentials and their superpositions, including the familiar H\'enon-Heiles problem. It is shown that SLO's can exist for arbitrary finite superpositions of $N$-forms. The results are applied to a family of generalized H\'enon-Heiles potentials having discrete rotational symmetry. SLO's are also found for superpositions of these potentials.Comment: laTeX with 6 figure

A Multi-Epoch Study of the Radio Continuum Emission of Orion Source I: Constraints on the Disk Evolution of a Massive YSO and the Dynamical History of Orion BN/KL

We present new 7mm continuum observations of Orion BN/KL with the VLA. We resolve the emission from the protostar radio Source I and BN at several epochs. Source I is highly elongated NW-SE, and remarkably stable in flux density, position angle, and overall morphology over nearly a decade. This favors the extended emission component arising from an ionized disk rather than a jet. We have measured the proper motions of Source I and BN for the first time at 43 GHz. We confirm that both sources are moving at high speed (12 and 26 km/s, respectively) approximately in opposite directions, as previously inferred from measurements at lower frequencies. We discuss dynamical scenarios that can explain the large motions of both BN and Source I and the presence of disks around both. Our new measurements support the hypothesis that a close (~50 AU) dynamical interaction occurred around 500 years ago between Source I and BN as proposed by Gomez et al. From the dynamics of encounter we argue that Source I today is likely to be a binary with a total mass on the order of 20 Msun, and that it probably existed as a softer binary before the close encounter. This enables preservation of the original accretion disk, though truncated to its present radius of ~50 AU. N-body numerical simulations show that the dynamical interaction between a binary of 20 Msun total mass (I) and a single star of 10 Msun mass (BN) may lead to the ejection of both and binary hardening. The gravitational energy released in the process would be large enough to power the wide-angle flow traced by H2 and CO emission in the BN/KL nebula. Assuming the proposed dynamical history is correct, the smaller mass for Source I recently estimated from SiO maser dynamics (>7 Msun) by Matthews et al., suggests that non-gravitational forces (e.g. magnetic) must play an important role in the circumstellar gas dynamics.Comment: 17 pages, 7 figures, 4 tables, accepted by Ap

Action minimizing orbits in the n-body problem with simple choreography constraint

In 1999 Chenciner and Montgomery found a remarkably simple choreographic motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal masses travel on a eight shaped planar curve; this orbit is obtained minimizing the action integral on the set of simple planar choreographies with some special symmetry constraints. In this work our aim is to study the problem of $n$ masses moving in \RR^d under an attractive force generated by a potential of the kind $1/r^\alpha$, $\alpha >0$, with the only constraint to be a simple choreography: if $q_1(t),...,q_n(t)$ are the $n$ orbits then we impose the existence of x \in H^1_{2 \pi}(\RR,\RR^d) such that q_i(t)=x(t+(i-1) \tau), i=1,...,n, t \in \RR, where $\tau = 2\pi / n$. In this setting, we first prove that for every d,n \in \NN and $\alpha>0$, the lagrangian action attains its absolute minimum on the planar circle. Next we deal with the problem in a rotating frame and we show a reacher phenomenology: indeed while for some values of the angular velocity minimizers are still circles, for others the minima of the action are not anymore rigid motions.Comment: 24 pages; 4 figures; submitted to Nonlinearit

The Effects of Clumps in Explaining X-ray Emission Lines from Hot Stars

It is now well established that stellar winds of hot stars are fragmentary and that the X-ray emission from stellar winds has a strong contribution from shocks in winds. Chandra high spectral resolution observations of line profiles of O and B stars have shown numerous properties that had not been expected. Here we suggest explanations by considering the X-rays as arising from bow shocks that occur where the stellar wind impacts on spherical clumps in the winds. We use an accurate and stable numerical hydrodynamical code to obtain steady-state physical conditions for the temperature and density structure in a bow shock. We use these solutions plus analytic approximations to interpret some major X-ray features: the simple power-law distribution of the observed emission measure derived from many hot star X-ray spectra and the wide range of ionization stages that appear to be present in X-ray sources throughout the winds. Also associated with the adiabatic cooling of the gas around a clump is a significant transverse velocity for the hot plasma flow around the clumps, and this can help to understand anomalies associated with observed line widths, and the differences in widths seen in stars with high and low mass-loss rates. The differences between bow shocks and the planar shocks that are often used for hot stars are discussed. We introduce an ``on the shock'' (OTSh) approximation that is useful for interpreting the X-rays and the consequences of clumps in hot star winds and elsewhere in astronomy.Comment: to appear in the Astrophysical Journa

Many-body localization and thermalization in the full probability distribution function of observables

We investigate the relation between thermalization following a quantum quench and many-body localization in quasiparticle space in terms of the long-time full distribution function of physical observables. In particular, expanding on our recent work [E. Canovi {\em et al.}, Phys. Rev. B {\bf 83}, 094431 (2011)], we focus on the long-time behavior of an integrable XXZ chain subject to an integrability-breaking perturbation. After a characterization of the breaking of integrability and the associated localization/delocalization transition using the level spacing statistics and the properties of the eigenstates, we study the effect of integrability-breaking on the asymptotic state after a quantum quench of the anisotropy parameter, looking at the behavior of the full probability distribution of the transverse and longitudinal magnetization of a subsystem. We compare the resulting distributions with those obtained in equilibrium at an effective temperature set by the initial energy. We find that, while the long time distribution functions appear to always agree {\it qualitatively} with the equilibrium ones, {\it quantitative} agreement is obtained only when integrability is fully broken and the relevant eigenstates are diffusive in quasi-particle space.Comment: 18 pages, 11 figure