A three-dimensional view of the remnant of Nova Persei 1901 (GK Per)

We present a kinematical study of the optical ejecta of GK Per. It is based on proper motions measurements of 282 knots from ~20 images spanning 25 years. Doppler-shifts are also computed for 217 knots. The combination of proper motions and radial velocities allows a unique 3-D view of the ejecta to be obtained. The main results are: (1) the outflow is a thick shell in which knots expand with a significant range of velocities, mostly between 600 and 1000 km/s; (2) kinematical ages indicate that knots have suffered only a modest deceleration since their ejection a century ago; (3) no evidence for anisotropy in the expansion rate is found; (4) velocity vectors are generally aligned along the radial direction but a symmetric pattern of non-radial velocities is also observed at specific directions; (5) the total Halpha+[NII] flux has been linearly decreasing at a rate of 2.6 % per year in the last decade. The Eastern nebular side is fading at a slower rate than the Western one. Some of the knots displayed a rapid change of brightness during the 2004-2011 period. Over a longer timescale, a progressive circularization and homogenization of the nebula is taking place; (6) a kinematic distance of 400+-30 pc is determined. These results raise some problems to the previous interpretations of the evolution of GK Per. In particular, the idea of a strong interaction of the outflow with the surrounding medium in the Southwest quadrant is not supported by our data.Comment: Accepted for publication in The Astrophysical Journal (19 pages, 17 figures). Higher resolution version of this article (2.5 MB) is available at http://www.aai.ee/~sinope/ApJ89291_liimets.pd

Lagrangian Formalism for nonlinear second-order Riccati Systems: one-dimensional Integrability and two-dimensional Superintegrability

The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are nonnatural and the forces are not derivable from a potential. The constant value $E$ of a preserved energy function can be used as an appropriate parameter for characterizing the behaviour of the solutions of these two systems. In the second part the existence of two--dimensional versions endowed with superintegrability is proved. The explicit expressions of the additional integrals are obtained in both cases. Finally it is proved that the orbits of the second system, that represents a nonlinear oscillator, can be considered as nonlinear Lissajous figuresComment: 25 pages, 7 figure

Momentum-resolved evolution of the Kondo lattice into 'hidden-order' in URu2Si2

We study, using high-resolution angle-resolved photoemission spectroscopy, the evolution of the electronic structure in URu2Si2 at the Gamma, Z and X high-symmetry points from the high-temperature Kondo-screened regime to the low-temperature `hidden-order' (HO) state. At all temperatures and symmetry points, we find structures resulting from the interaction between heavy and light bands, related to the Kondo lattice formation. At the X point, we directly measure a hybridization gap of 11 meV already open at temperatures above the ordered phase. Strikingly, we find that while the HO induces pronounced changes at Gamma and Z, the hybridization gap at X does not change, indicating that the hidden-order parameter is anisotropic. Furthermore, at the Gamma and Z points, we observe the opening of a gap in momentum in the HO state, and show that the associated electronic structure results from the hybridization of a light electron band with the Kondo-lattice bands characterizing the paramagnetic state.Comment: Updated published version. Mansucript + Supplemental Material (8 pages, 9 figures). Submitted 16 September 201

New insights into the outflows from R Aquarii

R Aquarii is a symbiotic binary surrounded by a large and complex nebula with a prominent curved jet. It is one of the closest known symbiotic systems, and therefore offers a unique opportunity to study the central regions of these systems and the formation and evolution of astrophysical jets. We studied the evolution of the central jet and outer nebula of R Aqr taking advantage of a long term monitoring campaign of optical imaging, as well as of high-resolution integral field spectroscopy. Narrow-band images acquired over a period of more than 21 years are compared in order to study the expansion and evolution of all components of the R Aqr nebula. The magnification method is used to derive the kinematic ages of the features that appear to expand radially. Integral field spectroscopy of the OIII 5007A emission is used to study the velocity structure of the central regions of the jet. New extended features, further out than the previously known hourglass nebula, are detected. The kinematic distance to R Aqr is calculated to be 178 pc using the expansion of the large hourglass nebula. This nebula of R Aqr is found to be roughly 650 years old, while the inner regions have ages ranging from 125 to 290 years. The outer nebula is found to be well described by a ballistic expansion, while for most components of the jet strong deviations from such behaviour are found. We find that the Northern jet is mostly red-shifted while its Southern part is blue-shifted, apparently at odds with findings from previous studies but almost certainly a consequence of the complex nature of the jet and variations in ionisation and illumination between observations.Comment: 13 pages, 8 figures, accepted for publication in A&

Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2S^2 and the hyperbolic plane H2H^2

The Kepler problem is a dynamical system that is well defined not only on the Euclidean plane but also on the sphere and on the Hyperbolic plane. First, the theory of central potentials on spaces of constant curvature is studied. All the mathematical expressions are presented using the curvature \k as a parameter, in such a way that they reduce to the appropriate property for the system on the sphere $S^2$, or on the hyperbolic plane $H^2$, when particularized for \k>0, or \k<0, respectively; in addition, the Euclidean case arises as the particular case \k=0. In the second part we study the main properties of the Kepler problem on spaces with curvature, we solve the equations and we obtain the explicit expressions of the orbits by using two different methods: first by direct integration and second by obtaining the \k-dependent version of the Binet's equation. The final part of the article, that has a more geometric character, is devoted to the study of the theory of conics on spaces of constant curvature.Comment: 37 pages, 7 figure

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Model-Independent Sum Rule Analysis Based on Limited-Range Spectral Data

Partial sum rules are widely used in physics to separate low- and high-energy degrees of freedom of complex dynamical systems. Their application, though, is challenged in practice by the always finite spectrometer bandwidth and is often performed using risky model-dependent extrapolations. We show that, given spectra of the real and imaginary parts of any causal frequency-dependent response function (for example, optical conductivity, magnetic susceptibility, acoustical impedance etc.) in a limited range, the sum-rule integral from zero to a certain cutoff frequency inside this range can be safely derived using only the Kramers-Kronig dispersion relations without any extra model assumptions. This implies that experimental techniques providing both active and reactive response components independently, such as spectroscopic ellipsometry in optics, allow an extrapolation-independent determination of spectral weight 'hidden' below the lowest accessible frequency.Comment: 5 pages, 3 figure