Detection of a strong transient blue-shifted absorption component in the beta Pictoris disk

We present high-resolution spectra (1.0 km s-1 FWHM) of the circumstellar Ca K line towards ß Pictoris obtained on 1997 June 19 and 20. On the former date a strong absorption component was found at a heliocentric velocity of vhelio = +8 km s-1, that is blueshifted by 14 km s-1 with respect to the main, ‘stable’, circumstellar component at vhelio = +22 km s-1. To our knowledge, this is the first detection of a blueshifted Ca II component with a strength comparable to the more frequently observed redshifted events. On the following night a blueshifted component was still present, but its strength had decreased significantly; in addition, a strong redshifted component had appeared at vhelio = +54 km s-1 which was absent on the previous night. The implications of these observations for the evaporating ‘comet’ model of spectral variations in the ß Pictoris disc are discussed

Ultra-high-resolution observations of Ca K line variations in the β Pictoris disc

We present observations of the β Pictoris circumstellar Ca II K line, obtained with the new Ultra-High-Resolution facility (UHRF) at the Anglo-Australian Telescope. The resolving power was R≳900000⁠, and these data therefore comprise the highest resolution observations yet obtained of this object. Observations were obtained on three nights in 1993 (May 11, August 26 and August 29), and significant temporal variability was observed, including previously unobserved changes in the profile of the main circumstellar component

Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories

We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, that can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form, so as to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that is at basis of the analytic part of the Nekhoroshev's theorem, so as to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with arXiv:1010.260

Euler configurations and quasi-polynomial systems

In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.Comment: 21 pages, 6 figure

The Hamiltonian formulation of General Relativity: myths and reality

A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in "Gravitation: An Introduction to Current Research" (1962) 227] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i-iii) have been shown to be incorrect in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric $g_{\mu\nu}$ to lapse and shift functions and the three-metric $g_{km}$, which is not canonical. This proves that point (iv) is incorrect. Points (i-iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein's theory itself.Comment: References are added and updated, Introduction is extended, Subsection 3.5 is added, 83 pages; corresponds to the published versio

Exocomets size distribution in the β Pictoris planetary system

Stars and planetary system