Models of cuspy triaxial stellar systems. III: The effect of velocity anisotropy on chaoticity

In several previous investigations we presented models of triaxial stellar systems, both cuspy and non cuspy, that were highly stable and harboured large fractions of chaotic orbits. All our models had been obtained through cold collapses of initially spherical $N$--body systems, a method that necessarily results in models with strongly radial velocity distributions. Here we investigate a different method that was reported to yield cuspy triaxial models with virtually no chaos. We show that such result was probably due to the use of an inadequate chaos detection technique and that, in fact, models with significant fractions of chaotic orbits result also from that method. Besides, starting with one of the models from the first paper in this series, we obtained three different models by rendering its velocity distribution much less radially biased (i.e., more isotropic) and by modifying its axial ratios through adiabatic compression. All three models yielded much higher fractions of regular orbits than most of those from our previous work. We conclude that it is possible to obtain stable cuspy triaxial models of stellar systems whose velocity distribution is more isotropic than that of the models obtained from cold collapses. Those models still harbour large fractions of chaotic orbits and, although it is difficult to compare the results from different models, we can tentatively conclude that chaoticity is reduced by velocity isotropy.Comment: 11 pages, 14 figures. Accepted for publication in MNRA

Optimal combinations of acute phase proteins for detecting infectious disease in pigs

Peer reviewedPublisher PD

Dissipationless Collapse of Spherical Protogalaxies and the Fundamental Plane

Following on from the numerical work of Capelato, de Carvalho & Carlberg (1995, 1997), where dissipationless merger simulations were shown to reproduce the "Fundamental Plane" (FP) of elliptical galaxies, we investigate whether the end products of pure, spherically symmetric, one-component dissipationless {\it collapses} could also reproduce the FP. Past numerical work on collisionless collapses have addressed important issues on the dynamical/structural characteristics of collapsed equilibrium systems. However, the study of collisionless collapse in the context of the nature of the FP has not been satisfactorily addressed yet. Our aim in this paper is to focus our attention on the resulting collapse of simple one-component spherical models with a range of different initial virial coefficients. We find that the characteristic correlations of the models are compatible with virialized, centrally homologous systems. Our results strengthen the idea that merging may be a fundamental ingredient in forming non-homologous objects.Comment: 9 pages, 4 Postscript figures, Astronomy & Astrophysics in press (2002). Abstract placement correcte

Numerical integration of variational equations

We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom, and investigate their efficiency in accurately reproducing well-known properties of chaos indicators like the Lyapunov Characteristic Exponents (LCEs) and the Generalized Alignment Indices (GALIs). We find that the best numerical performance is exhibited by the \textit{`tangent map (TM) method'}, a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy. According to this method, a symplectic integrator is used to approximate the solution of the Hamilton's equations of motion by the repeated action of a symplectic map $S$, while the corresponding tangent map $TS$, is used for the integration of the variational equations. A simple and systematic technique to construct $TS$ is also presented.Comment: 27 pages, 11 figures, to appear in Phys. Rev.

Probing a regular orbit with spectral dynamics

We have extended the spectral dynamics formalism introduced by Binney & Spergel, and have implemented a semi-analytic method to represent regular orbits in any potential, making full use of their regularity. We use the spectral analysis code of Carpintero & Aguilar to determine the nature of an orbit (irregular, regular, resonant, periodic) from a short-time numerical integration. If the orbit is regular, we approximate it by a truncated Fourier time series of a few tens of terms per coordinate. Switching to a description in action-angle variables, this corresponds to a reconstruction of the underlying invariant torus. We then relate the uniform distribution of a regular orbit on its torus to the non-uniform distribution in the space of observables by a simple Jacobian transformation between the two sets of coordinates. This allows us to compute, in a cell-independent way, all the physical quantities needed in the study of the orbit, including the density and in the line-of-sight velocity distribution, with much increased accuracy. The resulting flexibility in the determination of the orbital properties, and the drastic reduction of storage space for the orbit library, provide a significant improvement in the practical application of Schwarzschild's orbit superposition method for constructing galaxy models. We test and apply our method to two-dimensional orbits in elongated discs, and to the meridional motion in axisymmetric potentials, and show that for a given accuracy, the spectral dynamics formalism requires an order of magnitude fewer computations than the more traditional approaches.Comment: 13 pages, 18 eps figures, submitted to MNRA

Building up the Stellar Halo of the Galaxy

We study numerical simulations of satellite galaxy disruption in a potential resembling that of the Milky Way. Our goal is to assess whether a merger origin for the stellar halo would leave observable fossil structure in the phase-space distribution of nearby stars. We show how mixing of disrupted satellites can be quantified using a coarse-grained entropy. Although after 10 Gyr few obvious asymmetries remain in the distribution of particles in configuration space, strong correlations are still present in velocity space. We give a simple analytic description of these effects, based on a linearised treatment in action-angle variables, which shows how the kinematic and density structure of the debris stream changes with time. By applying this description we find that a single satellite of current luminosity 10^8 L_\sun disrupted 10 Gyr ago from an orbit circulating in the inner halo (mean apocentre $\sim 12$ kpc) would contribute about $\sim 30$ kinematically cold streams with internal velocity dispersions below 5 km/s to the local stellar halo. If the whole stellar halo were built by disrupted satellites, it should consist locally of 300 - 500 such streams. Clear detection of all these structures would require a sample of a few thousand stars with 3-D velocities accurate to better than 5 km/s. Even with velocity errors several times worse than this, the expected clumpiness should be quite evident. We apply our formalism to a group of stars detected near the North Galactic Pole, and derive an order of magnitude estimate for the initial properties of the progenitor system.Comment: 28 pages, 10 figures, minor changes, matches the version to appear in MNRAS, Vol. 307, p.495-517 (August 1999

The length of stellar bars in SB galaxies and N-body simulations

We have investigated the accuracy and reliability of six methods used to determine the length of stellar bars in galaxies or N-body simulations. All these methods use ellipse fitting and Fourier decomposition of the surface brightness. We have applied them to N-body simulations that include stars, gas, star formation, and feedback. Stellar particles were photometrically calibrated to make B and K-band mock images. Dust absorption is also included. We discuss the advantages and drawbacks of each method, the effects of projection and resolution, as well as the uncertainties introduced by the presence of dust. The use of N-body simulations allows us to compare the location of Ultra Harmonic Resonance (UHR or 4/1) and corotation (CR) with measured bar lengths. We show that the minimum of ellipticity located just outside the bulk of the bar is correlated with the corotation, whereas the location of the UHR can be approximated using the phase of the fitted ellipses or the phase of the m=2 Fourier development of the surface brightness. We give evidence that the classification of slow/fast bars, based on the ratio R = Rcr/Rbar could increase from 1 (fast bar) to 1.4 (slow bar) just by a change of method. We thus conclude that one has to select the right bar-length estimator depending on the application, since these various estimators do not define the same physical area.Comment: Major revision, A&A in pres

Comparison of the bifurcation scenarios predicted by the single-mode and multimode semiconductor laser rate equations

We present a detailed comparison of the bifurcation scenarios predicted by single-mode and multimode semiconductor laser rate equation models under large amplitude injection current modulation. The influence of the gain model on the predicted dynamics is investigated. Calculations of the dependence of the time averaged longitudinal mode intensities on modulation frequency are compared with experiments performed on an AlxGa1-xAs Fabry-Pérot semiconductor laser.K. A. Corbett and M. W. Hamilto

Pig α₁-Acid Glycoprotein: Characterization and First Description in Any Species as a Negative Acute Phase Protein.

The serum protein α1-acid glycoprotein (AGP), also known as orosomucoid, is generally described as an archetypical positive acute phase protein. Here, porcine AGP was identified, purified and characterized from pooled pig serum. It was found to circulate as a single chain glycoprotein having an apparent molecular weight of 43 kDa by SDS-PAGE under reducing conditions, of which approximately 17 kDa were accounted for by N-bound oligosaccharides. Those data correspond well with the properties of the protein predicted from the single porcine AGP gene (ORM1, Q29014 (UniProt)), containing 5 putative glycosylation sites. A monoclonal antibody (MAb) was produced and shown to quantitatively and specifically react with all microheterogenous forms of pig AGP as analyzed by 2-D electrophoresis. This MAb was used to develop an immunoassay (ELISA) for quantification of AGP in pig serum samples. The adult serum concentrations of pig AGP were in the range of 1-3 mg/ml in a number of conventional pig breeds while it was lower in Göttingen and Ossabaw minipigs (in the 0.3 to 0.6 mg/ml range) and higher in young (2-5 days old) conventional pigs (mean: 6.6 mg/ml). Surprisingly, pig AGP was found to behave as a negative acute phase protein during a range of experimental infections and aseptic inflammation with significant decreases in serum concentration and in hepatic ORM1 expression during the acute phase response. To our knowledge this is the first description in any species of AGP being a negative acute phase protein