The three-dimensional structure of the Eta Carinae Homunculus

We investigate, using the modeling code SHAPE, the three-dimensional structure of the bipolar Homunculus nebula surrounding Eta Carinae, as mapped by new ESO VLT/X-Shooter observations of the H2 $\lambda=2.12125$ micron emission line. Our results reveal for the first time important deviations from the axisymmetric bipolar morphology: 1) circumpolar trenches in each lobe positioned point-symmetrically from the center and 2) off-planar protrusions in the equatorial region from each lobe at longitudinal (~55 degrees) and latitudinal (10-20 degrees) distances from the projected apastron direction of the binary orbit. The angular distance between the protrusions (~110 degrees) is similar to the angular extent of each polar trench (~130 degrees) and nearly equal to the opening angle of the wind-wind collision cavity (~110 degrees). As in previous studies, we confirm a hole near the centre of each polar lobe and no detectable near-IR H2 emission from the thin optical skirt seen prominently in visible imagery. We conclude that the interaction between the outflows and/or radiation from the central binary stars and their orientation in space has had, and possibly still has, a strong influence on the Homunculus. This implies that prevailing theoretical models of the Homunculus are incomplete as most assume a single star origin that produces an axisymmetric nebula. We discuss how the newly found features might be related to the Homunculus ejection, the central binary and the interacting stellar winds. We also include a 3D printable version of our Homunculus model.Comment: 14 pages, 7 color figures, 1 interactive 3D figure (Figure 5, requires Adobe Reader), published in MNRAS. A 3D printable version of our Homunculus model can be downloaded from http://svs.gsfc.nasa.gov/vis/a010000/a011500/a011568/Eta_Car_Homunuculus_3D_model.zip or from the 'Supporting Information' link in the electronic version of the MNRAS articl

aristotle's demonstrative logic

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogisti

Constraints on decreases in Eta Carinae's mass loss from 3D hydrodynamic simulations of its binary colliding winds

Recent work suggests that the mass-loss rate of the primary star (Eta A) in the massive colliding wind binary Eta Carinae dropped by a factor of 2-3 between 1999 and 2010. We present results from large- (r=1545au) and small- (r=155au) domain, 3D smoothed particle hydrodynamic (SPH) simulations of Eta Car's colliding winds for 3 Eta A mass-loss rates (2.4, 4.8, and 8.5 x 10^-4 M_sun/yr), investigating the effects on the dynamics of the binary wind-wind collision (WWC). These simulations include orbital motion, optically thin radiative cooling, and radiative forces. We find that Eta A's mass-loss rate greatly affects the time-dependent hydrodynamics at all spatial scales investigated. The simulations also show that the post-shock wind of the companion star (Eta B) switches from the adiabatic to the radiative-cooling regime during periastron passage. The SPH simulations together with 1D radiative transfer models of Eta A's spectra reveal that a factor of 2 or more drop in Eta A's mass-loss rate should lead to substantial changes in numerous multiwavelength observables. Recent observations are not fully consistent with the model predictions, indicating that any drop in Eta A's mass-loss rate was likely by a factor < 2 and occurred after 2004. We speculate that most of the recent observed changes in Eta Car are due to a small increase in the WWC opening angle that produces significant effects because our line-of-sight to the system lies close to the dense walls of the WWC zone. A modest decrease in Eta A's mass-loss rate may be responsible, but changes in the wind/stellar parameters of Eta B cannot yet be fully ruled out. We suggest observations during Eta Car's next periastron in 2014 to further test for decreases in Eta A's mass-loss rate. If Eta A's mass-loss rate is declining and continues to do so, the 2014 X-ray minimum should be even shorter than that of 2009.Comment: 38 pages, 25 figures, 1 table. Accepted for publication in MNRA

Coherence in the Quasi-Particle 'Scattering' by the Vortex Lattice in Pure Type-II Superconductors

The effect of quasi-particle (QP) 'scattering' by the vortex lattice on the de-Haas van-Alphen oscillations in a pure type-II superconductor is investigated within mean field,asymptotic perturbation theory. Using a 2D electron gas model it is shown that, due to a strict phase coherence in the many-particle correlation functions, the 'scattering' effect in the asymptotic limit ($\sqrt{E_F/\hbar\omega_c}\gg 1$) is much weaker than what is predicted by the random vortex lattice model proposed by Maki and Stephen, which destroys this coherence . The coherent many particle configuration is a collinear array of many particle coordinates, localized within a spatial region with size of the order of the magnetic length. The amplitude of the magnetization oscillations is sharply damped just below $$ because of strong $180^{\circ}$ out of phase magnetic oscillations in the superconducting condensation energy ,which tend to cancel the normal electron oscillations. Within the ideal 2D model used it is found, however, that because of the relative smallness of the quartic and higher order terms in the expansion, the oscillations amplitude at lower fields does not really damp to zero, but only reverses sign and remains virtually undamped well below $H_{c2}$. This conclusion may be changed if disorder in the vortex lattice, or vortex lines motion will be taken into account. The reduced QP 'scattering' effect may be responsible for the apparent crossover from a strong damping of the dHvA oscillations just below $H_{c2}$ to a weaker damping at lower fields observed experimentally in several 3D superconductors.Comment: 26 pages, Revtex no Figure

Density of states of a type-II superconductor in a high magnetic field: Impurity effects

We have calculated the density of states $N(\omega)$ of a dirty but homogeneous superconductor in a high magnetic field. We assume a dilute concentration of scalar impurities and find how $N(\omega)$ behaves as one crosses from the weak scattering to the strong scattering limit. At low energies, $N(\omega)\sim \omega ^2$ for small values of the impurity concentration and scattering strength. When the disorder becomes stronger than some critical value, a finite density of states is created at the Fermi surface. These results are a consequence of the gapless nature of the quasiparticle excitation spectrum in a high magnetic field.Comment: 20 pages in RevTeX, 4 figures, to appear in Phys. Rev. B (July 1, 1997

An adaptive Metropolis-Hastings scheme: sampling and optimization

We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field approximation to the target distribution, and update the proposal distribution to be that approximatio. We employ our algorithm to sample the energy distribution for several spin-glasses and we demonstrate the superiority of our algorithm to the conventional MH algorithm in sampling and in annealing optimization.Comment: To appear in Europhysics Letter

Detection of high-velocity material from the wind-wind collision zone of Eta Carinae across the 2009.0 periastron passage

We report near-IR spectroscopic observations of the Eta Carinae massive binary system during 2008-2009 using VLT/CRIRES. We detect a strong, broad absorption wing in He I 10833 extending up to -1900 km/s across the 2009.0 spectroscopic event. Archival HST/STIS ultraviolet and optical data shows a similar high-velocity absorption (up to -2100 km/s) in the UV resonance lines of Si IV 1394, 1403 across the 2003.5 event. UV lines from low-ionization species, such as Si II 1527, 1533 and C II 1334, 1335, show absorption up to -1200 km/s, indicating that the absorption with v from -1200 to -2100 km/s originates in a region markedly faster and more ionized than the nominal wind of the primary star. Observations obtained at the OPD/LNA during the last 4 spectroscopic cycles (1989-2009) also display high-velocity absorption in He I 10833 during periastron. Based on the OPD/LNA dataset, we determine that material with v < -900 km/s is present in the phase range 0.976 < phi < 1.023 of the spectroscopic cycle, but absent in spectra taken at phi < 0.947 and phi > 1.049. Therefore, we constrain the duration of the high-velocity absorption to be 95 to 206 days (or 0.047 to 0.102 in phase). We suggest that the high-velocity absorption originates from shocked gas in the wind-wind collision zone, at distances of 15 to 45 AU in the line-of-sight to the primary star. Using 3-D hydrodynamical simulations of the wind-wind collision zone, we find that the dense high-velocity gas is in the line-of-sight to the primary star only if the binary system is oriented in the sky so that the companion is behind the primary star during periastron, corresponding to a longitude of periastron of omega ~ 240 to 270 degrees. We study a possible tilt of the orbital plane relative to the Homunculus equatorial plane and conclude that our data are broadly consistent with orbital inclinations in the range i=40 to 60 degrees.Comment: 18 pages, 15 figures, accepted for publication in A&A; high-resolution PDF version available also at http://www.mpifr.de/staff/jgroh/etacar.htm

Absence of Persistent Magnetic Oscillations in Type-II Superconductors

We report on a numerical study intended to examine the possibility that magnetic oscillations persist in type II superconductors beyond the point where the pairing self-energy exceeds the normal state Landau level separation. Our work is based on the self-consistent numerical solution for model superconductors of the Bogoliubov-deGennes equations for the vortex lattice state. In the regime where the pairing self-energy is smaller than the cyclotron energy, magnetic oscillations resulting from Landau level quantization are suppressed by the broadening of quasiparticle Landau levels due to the non-uniform order parameter of the vortex lattice state, and by splittings of the quasiparticle bands. Plausible arguments that the latter effect can lead to a sign change of the fundamental harmonic of the magnetic oscillations when the pairing self-energy is comparable to the cyclotron energy are shown to be flawed. Our calculations indicate that magnetic oscillations are strongly suppressed once the pairing self-energy exceeds the Landau level separation.Comment: 7 pages, revtex, 7 postscript figure

Ginzburg-Landau-Gor'kov Theory of Magnetic oscillations in a type-II 2-dimensional Superconductor

We investigate de Haas-van Alphen (dHvA) oscillations in the mixed state of a type-II two-dimensional superconductor within a self-consistent Gor'kov perturbation scheme. Assuming that the order parameter forms a vortex lattice we can calculate the expansion coefficients exactly to any order. We have tested the results of the perturbation theory to fourth and eight order against an exact numerical solution of the corresponding Bogoliubov-de Gennes equations. The perturbation theory is found to describe the onset of superconductivity well close to the transition point $H_{c2}$. Contrary to earlier calculations by other authors we do not find that the perturbative scheme predicts any maximum of the dHvA-oscillations below $H_{c2}$. Instead we obtain a substantial damping of the magnetic oscillations in the mixed state as compared to the normal state. We have examined the effect of an oscillatory chemical potential due to particle conservation and the effect of a finite Zeeman splitting. Furthermore we have investigated the recently debated issue of a possibility of a sign change of the fundamental harmonic of the magnetic oscillations. Our theory is compared with experiment and we have found good agreement.Comment: 39 pages, 8 figures. This is a replacement of supr-con/9608004. Several sections changed or added, including a section on the effect of spin and the effect of a conserved number of particles. To be published in Phys. Rev.

Evolution of emission line activity in intermediate mass young stars

We present optical spectra of 45 intermediate mass Herbig Ae/Be stars. Together with the multi-epoch spectroscopic and photometric data compiled for a large sample of these stars and ages estimated for individual stars by using pre-main sequence evolutionary tracks, we have studied the evolution of emission line activity in them. We find that, on average, the H_alpha emission line strength decreases with increasing stellar age in HAeBe stars, indicating that the accretion activity gradually declines during the PMS phase. This would hint at a relatively long-lived (a few Myr) process being responsible for the cessation of accretion in Herbig Ae/Be stars. We also find that the accretion activity in these stars drops substantially by ~ 3 Myr. This is comparable to the timescale in which most intermediate mass stars are thought to lose their inner disks, suggesting that inner disks in intermediate mass stars are dissipated rapidly after the accretion activity has fallen below a certain level. We, further find a relatively tight correlation between strength of the emission line and near-infrared excess due to inner disks in HAeBe stars, indicating that the disks around Herbig Ae/Be stars cannot be entirely passive. We suggest that this correlation can be understood within the frame work of the puffed-up inner rim disk models if the radiation from the accretion shock is also responsible for the disk heating.Comment: 39 pages, accepted for publication in Ap