On the variational approach to the periodic n-body problem

This expository paper gathers some of the results obtained by the author in recent works in collaboration with Davide Ferrario and Vivina Barutello, focusing on the periodic n-body problem from the perspective of the calculus of variations and minimax theory. These researches were aimed at developing a systematic variational approach to the equivariant periodic n-body problem in the two and three-dimensional space. The purpose of this paper is to expose the main problems and achievements of this approach. The material here was exposed in the talk that given at the Meeting CELMEC IV promoted by SIMCA (Società italiana di Meccanica Celeste).     

Optical Spectroscopy of Comet C/2000 WM1 (LINEAR) at the Guillermo Harro Astrophysical Observatory in Mexico

We present a preliminary analysis of medium resolution optical spectra of comet C/2000 WM1 (LINEAR) obtained on 22 November 2001. Theemission lines of the molecules C₂, C₃, CN, NH₂,H₂O⁺ and presumably CO (Asundi and triplet bands) and C₂ ^-were identified in these spectra. By analysing the brightnessdistributions of the C₂, C₃, CN emission lines along theslit of the spectrograph we determined some physical parameters of theseneutrals, such as their lifetimes and expansion velocities inthe coma. The Franck–Condon factors for the CO Asundi bands and C₂ ^- bands were calculated using a Morse potential model.     

Chandra observations of neutron stars: an overview

We present an overview of Chandra X-ray Observatory observations of neutron stars. The outstanding spatial and spectral resolution of this great observatory have allowed for observations of unprecedented clarity and accuracy. Many of these observations have provided new insights into neutron star physics. We present an admittedly biased and overly brief review of these observations, highlighting some new discoveries made possible by the Observatory’s unique capabilities. This includes our analysis of recent multiwavelength observations of the putative pulsar and its pulsar-wind nebula in the IC443 SNR.      

A MERLIN survey of 4.7-GHz excited OH masers in star-forming regions

Phase-referenced observations of 13 star-forming regions in the  ²Π_1/2, J = 1/2  transition of rotationally excited OH at 4765 MHz have been carried out using MERLIN. Two of the regions were also observed at 4750 MHz and one at 4660 MHz. There were 10 maser detections at 4765 MHz and three non-detections. There were no detections at 4750 and 4660 MHz. The 4765-MHz masers have brightness temperatures of  ∼10⁷ K  at MERLIN resolution (∼50 mas). Several cases of 4765-MHz masers overlapping in position and velocity with 1720- and 1665-MHz masers are reported. There are also isolated 4765-MHz masers with peak flux densities ≥30 times that of any ground-state counterpart. Most of the 4.7-GHz maser spots are unresolved at 50-mas angular resolution, but in four of the nearest sources the maser spots are resolved, indicating a characteristic size for 4765-MHz maser regions of ∼100 au. In W3(OH) we discovered that 20 per cent of the 4765-MHz emission comes from a narrow low-brightness filament that stretches north–south for ∼1.0 arcec (∼2200 au) between two previously known 4765-MHz maser spots. The filament appears in projection against the H  ii region and has a brightness temperature of  ∼4 × 10⁵ K  . There are matching absorption features in mainline transitions of highly excited OH. The filament may trace a shock front in a rotating disc.     

Stability of motion in the Sitnikov 3-body problem

We study the stability of motion in the 3-body Sitnikov problem, with the two equal mass primaries (m ₁ = m ₂ = 0.5) rotating in the x, y plane and vary the mass of the third particle, 0 ≤ m ₃ < 10⁻³, placed initially on the z-axis. We begin by finding for the restricted problem (with m ₃ = 0) an apparently infinite sequence of stability intervals on the z-axis, whose width grows and tends to a fixed non-zero value, as we move away from z = 0. We then estimate the extent of “islands” of bounded motion in x, y, z space about these intervals and show that it also increases as |z| grows. Turning to the so-called extended Sitnikov problem, where the third particle moves only along the z-axis, we find that, as m ₃ increases, the domain of allowed motion grows significantly and chaotic regions in phase space appear through a series of saddle-node bifurcations. Finally, we concentrate on the general 3-body problem and demonstrate that, for very small masses, m ₃ ≈ 10⁻⁶, the “islands” of bounded motion about the z-axis stability intervals are larger than the ones for m ₃ = 0. Furthermore, as m ₃ increases, it is the regions of bounded motion closest to z = 0 that disappear first, while the ones further away “disperse” at larger m ₃ values, thus providing further evidence of an increasing stability of the motion away from the plane of the two primaries, as observed in the m ₃ = 0 case.     

The Non-Linear Stability of L4 in the Restricted Three-Body Problem when the Bigger Primary is a Triaxial Rigid Body

The non-linear stability of L ₄ in the restricted three-body problem has been studied when the bigger primary is a triaxial rigid body with its equatorial plane coincident with the plane of motion. It is found that L ₄ is stable in the range of linear stability except for three mass ratios:

The aperiodic broad-band X-ray variability of Cygnus X-3

We study the soft X-ray variability of Cygnus X-3. By combining data from the All-Sky Monitor and Proportional Counter Array instruments on the RXTE satellite with EXOSAT /Medium Energy (ME) detector observations, we are able to analyse the power density spectrum (PDS) of the source from 10⁻⁹ to 0.1 Hz, thus covering time-scales from seconds to years. As the data on the longer time-scales are unevenly sampled, we combine traditional power spectral techniques with simulations to analyse the variability in this range. The PDS at higher frequencies  (≳10⁻³ Hz)  are for the first time compared for all states of this source. We find that it is for all states well described by a power law, with index  ∼−2  in the soft states and a tendency for a less steep power law in the hard state. At longer time-scales, we study the effect of the state transitions on the PDS, and find that the variability below  ∼10⁻⁷ Hz  is dominated by the transitions. Furthermore, we find no correlation between the length of a high/soft-state episode and the time since the previous high/soft state. On intermediate time-scales, we find evidence for a break in the PDS at time-scales of the order of the orbital period. This may be interpreted as evidence for the existence of a tidal resonance in the accretion disc around the compact object, and constraining the mass ratio to   M ₂/ M ₁≲ 0.3  .