Dynamics of triaxial galaxies with a central density cusp

Cuspy triaxial potentials admit a large number of chaotic orbits, which moreover exhibit extreme "stickiness" that makes the process of chaotic mixing surprisingly inefficient. Environmental effects, modeled as noise and/or periodic driving, help accelerate phase space transport but probably not as much as in simpler potentials. This could mean that cuspy triaxial ellipticals cannot exist as time-independent systems

Malignant metastasizing solitary fibrous tumors of the liver: a report of three cases.

Solitary fibrous tumors are rare neoplasms of mesenchymal origin that have been reported in various other extrathoracic sites, including the liver. We present a case series of three malignant solitary fibrous tumors of the liver, occurring in two women 74 and 80 years old and one 65-year-old man. No clinical features were predictive of malignancy except the large sizes and synchronous presence of lung metastases in two of the three cases. Histological examinations revealed the presence of high pleomorphic cellularity with nuclear atypia, necrosis and high mitotic ratios. All patients died of disease progression

Periodic Orbits and Escapes in Dynamical Systems

We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a general relativistic system). We find their simple periodic orbits, their characteristics and their stability. Then we find their ordered and chaotic domains. As the energy goes beyond the escape energy, most chaotic orbits escape. In the first case we consider escapes to infinity, while in the second case we emphasize escapes to the central "bumpy" black hole. When the energy reaches its escape value a particular family of periodic orbits reaches an infinite period and then the family disappears (the orbit escapes). As this family approaches termination it undergoes an infinity of equal period and double period bifurcations at transitions from stability to instability and vice versa. The bifurcating families continue to exist beyond the escape energy. We study the forms of the phase space for various energies, and the statistics of the chaotic and escaping orbits. The proportion of these orbits increases abruptly as the energy goes beyond the escape energy.Comment: 28 pages, 23 figures, accepted in "Celestial Mechanics and Dynamical Astronomy

Large-scale environments of binary AGB stars probed by Herschel. II: Two companions interacting with the wind of pi1 Gruis

Context. The Mass loss of Evolved StarS (MESS) sample observed with PACS on board the Herschel Space Observatory revealed that several asymptotic giant branch (AGB) stars are surrounded by an asymmetric circumstellar envelope (CSE) whose morphology is most likely caused by the interaction with a stellar companion. The evolution of AGB stars in binary systems plays a crucial role in understanding the formation of asymmetries in planetary nebul{\ae} (PNe), but at present, only a handful of cases are known where the interaction of a companion with the stellar AGB wind is observed. Aims. We probe the environment of the very evolved AGB star $\pi^1$ Gruis on large and small scales to identify the triggers of the observed asymmetries. Methods. Observations made with Herschel/PACS at 70 $\mu$m and 160 $\mu$m picture the large-scale environment of $\pi^1$ Gru. The close surroundings of the star are probed by interferometric observations from the VLTI/AMBER archive. An analysis of the proper motion data of Hipparcos and Tycho-2 together with the Hipparcos Intermediate Astrometric Data help identify the possible cause for the observed asymmetry. Results. The Herschel/PACS images of $\pi^1$ Gru show an elliptical CSE whose properties agree with those derived from a CO map published in the literature. In addition, an arc east of the star is visible at a distance of $38^{\prime\prime}$ from the primary. This arc is most likely part of an Archimedean spiral caused by an already known G0V companion that is orbiting the primary at a projected distance of 460 au with a period of more than 6200 yr. However, the presence of the elliptical CSE, proper motion variations, and geometric modelling of the VLTI/AMBER observations point towards a third component in the system, with an orbital period shorter than 10 yr, orbiting much closer to the primary than the G0V star.Comment: 13 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

A Quintet Of Black Hole Mass Determinations

We report five new measurements of central black hole masses based on Space Telescope Imaging Spectrograph and Wide Field Planetary Camera 2 observations with the Hubble Space Telescope (HST) and on axisymmetric, three-integral, Schwarzschild orbit-library kinematic models. We selected a sample of galaxies within a narrow range in velocity dispersion that cover a range of galaxy parameters (including Hubble type and core/power-law surface density profile) where we expected to be able to resolve the galaxy's sphere of influence based on the predicted value of the black hole mass from the M-sigma relation. We find masses for the following galaxies: NGC3585, M(BH) = 3.4(-0.6)(+1.5) x 10(8) M(circle dot;) NGC 3607, M(BH) = 1.2(-0.4)(+0.4) x 10(8) M(circle dot); NGC 4026, M(BH) = 2.1(-0.4)(+0.7) x 10(8) M(circle dot); and NGC 5576, M(BH) = 1.8(-0.4)(+0.3) x 10(8) M(circle dot), all significantly excluding M(BH) = 0. For NGC 3945, M(BH) = 9(-21)(+17) x 10(6) M(circle dot), which is significantly below predictions from M-sigma and M-L relations and consistent with MBH = 0, though the presence of a double bar in this galaxy may present problems for our axisymmetric code.NASA/HST GO-5999, GO-6587, GO-6633, GO-7468, GO-9107NASA NAS 5-26555Astronom

The M-sigma and M-L Relations in Galactic Bulges and Determinations of their Intrinsic Scatter

We derive improved versions of the relations between supermassive black hole mass (M_BH) and host-galaxy bulge velocity dispersion (sigma) and luminosity (L) (the M-sigma and M-L relations), based on 49 M_BH measurements and 19 upper limits. Particular attention is paid to recovery of the intrinsic scatter (epsilon_0) in both relations. We find log(M_BH / M_sun) = alpha + beta * log(sigma / 200 km/s) with (alpha, beta, epsilon_0) = (8.12 +/- 0.08, 4.24 +/- 0.41, 0.44 +/- 0.06) for all galaxies and (alpha, beta, epsilon_0) = (8.23 +/- 0.08, 3.96 +/- 0.42, 0.31 +/- 0.06) for ellipticals. The results for ellipticals are consistent with previous studies, but the intrinsic scatter recovered for spirals is significantly larger. The scatter inferred reinforces the need for its consideration when calculating local black hole mass function based on the M-sigma relation, and further implies that there may be substantial selection bias in studies of the evolution of the M-sigma relation. We estimate the M-L relationship as log(M_BH / M_sun) = alpha + beta * log(L_V / 10^11 L_sun,V) of (alpha, beta, epsilon_0) = (8.95 +/- 0.11, 1.11 +/- 0.18, 0.38 +/- 0.09); using only early-type galaxies. These results appear to be insensitive to a wide range of assumptions about the measurement errors and the distribution of intrinsic scatter. We show that culling the sample according to the resolution of the black hole's sphere of influence biases the relations to larger mean masses, larger slopes, and incorrect intrinsic residuals.Comment: 27 pages, 18 figures, 7 tables, ApJ accepte

Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model

We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in this system, as models with relatively strong bars were shown to exhibit stronger chaotic behavior compared to those having a weaker bar component. Here, we attempt to further explore this connection by studying the interplay between chaotic and regular behavior of star orbits when the parameters of the model evolve in time. This happens for example when one introduces linear time dependence in the mass parameters of the model to mimic, in some general sense, the effect of self-consistent interactions of the actual N-body problem. We thus observe, in this simple time-dependent model also, that the increase of the bar's mass leads to an increase of the system's chaoticity. We propose a new way of using the Generalized Alignment Index (GALI) method as a reliable criterion to estimate the relative fraction of chaotic vs. regular orbits in such time-dependent potentials, which proves to be much more efficient than the computation of Lyapunov exponents. In particular, GALI is able to capture subtle changes in the nature of an orbit (or ensemble of orbits) even for relatively small time intervals, which makes it ideal for detecting dynamical transitions in time-dependent systems.Comment: 21 pages, 9 figures (minor typos fixed) to appear in J. Phys. A: Math. Theo

Chaos and the continuum limit in the gravitational N-body problem II. Nonintegrable potentials

This paper continues a numerical investigation of orbits evolved in `frozen,' time-independent N-body realisations of smooth time-independent density distributions corresponding to both integrable and nonintegrable potentials, allowing for N as large as 300,000. The principal focus is on distinguishing between, and quantifying, the effects of graininess on initial conditions corresponding, in the continuum limit, to regular and chaotic orbits. Ordinary Lyapunov exponents X do not provide a useful diagnostic for distinguishing between regular and chaotic behaviour. Frozen-N orbits corresponding in the continuum limit to both regular and chaotic characteristics have large positive X even though, for large N, the `regular' frozen-N orbits closely resemble regular characteristics in the smooth potential. Viewed macroscopically both `regular' and `chaotic' frozen-N orbits diverge as a power law in time from smooth orbits with the same initial condition. There is, however, an important difference between `regular' and `chaotic' frozen-N orbits: For regular orbits, the time scale associated with this divergence t_G ~ N^{1/2}t_D, with t_D a characteristic dynamical time; for chaotic orbits t_G ~ (ln N) t_D. At least for N>1000 or so, clear distinctions exist between phase mixing of initially localised orbit ensembles which, in the continuum limit, exhibit regular versus chaotic behaviour. For both regular and chaotic ensembles, finite-N effects are well mimicked, both qualitatively and quantitatively, by energy-conserving white noise with amplitude ~ 1/N. This suggests strongly that earlier investigations of the effects of low amplitude noise on phase space transport in smooth potentials are directly relevant to real physical systems.Comment: 20 pages, including 21 FIGURES, uses RevTeX macro

A Stellar Dynamical Measurement of the Black Hole Mass in the Maser Galaxy NGC 4258

We determine the mass of the black hole at the center of the spiral galaxy NGC 4258 by constructing axisymmetric dynamical models of the galaxy. These models are constrained by high spatial resolution imaging and long-slit spectroscopy of the nuclear region obtained with the {\em Hubble Space Telescope}, complemented by ground-based observations extending to larger radii. Our best mass estimate is \MBH = (3.3 \pm 0.2) \times 10^7 \MSun for a distance of 7.28 Mpc (statistical errors only). This is within 15% of (3.82\pm 0.01) \times 10^7 \MSun, the mass determined from the kinematics of water masers (rescaled to the same distance) assuming they are in Keplerian rotation in a warped disk. The construction of accurate dynamical models of NGC 4258 is somewhat compromised by an unresolved active nucleus and color gradients, the latter caused by variations in the stellar population and/or obscuring dust. These problems are not present in the $\sim 30$ other black hole mass determinations from stellar dynamics that have been published by us and other groups; thus, the relatively close agreement between the stellar dynamical mass and the maser mass in NGC 4258 enhances our confidence in the black hole masses determined in other galaxies from stellar dynamics using similar methods and data of comparable quality.Comment: 58 pages, submitted to ApJ. Some figures excluded due to size. The entire paper is at http://www.noao.edu/noao/staff/lauer/nuker_papers.htm

The Impact of Gaia and LSST on Binaries and Exoplanets

Two upcoming large scale surveys, the ESA Gaia and LSST projects, will bring a new era in astronomy. The number of binary systems that will be observed and detected by these projects is enormous, estimations range from millions for Gaia to several tens of millions for LSST. We review some tools that should be developed and also what can be gained from these missions on the subject of binaries and exoplanets from the astrometry, photometry, radial velocity and their alert system