Statistical Theory of Asteroid Escape Rates

Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars. Theory and numerical simulations are found to agree to better than 1%. These calculations suggest that further development of transition state theory in celestial mechanics, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations

Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics

Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly. The quantum dynamics near the classical limit displays both exponential separation of adjacent distributions and long time relaxation, two characteristic features of classical chaotic motion.Comment: 10 pages, ReVTeX, to appear in Phys. Rev. Lett. 13 figures NOT included. Available either as LARGE (uuencoded gzipped) postscript files or hard-copies from [email protected]

BUDHIES I: characterizing the environments in and around two clusters at z~0.2

We present the optical spectroscopy for the Blind Ultra Deep HI Environmental Survey (BUDHIES). With the Westerbork Synthesis Radio Telescope, BUDHIES has detected HI in over 150 galaxies in and around two Abell clusters at z~0.2. With the aim of characterizing the environments of the HI-detected galaxies, we obtained multi-fiber spectroscopy with the William Herschel Telescope. In this paper, we describe the spectroscopic observations, report redshifts and EW[OII] measurements for ~600 galaxies, and perform an environmental analysis. In particular, we present cluster velocity dispersion measurements for 5 clusters and groups in the BUDHIES volume, as well as a detailed substructure analysis.Comment: v2: Typos and small corrections after proofs added. 14 pages (plus small appendix), 12 figures. Accepted for publication in MNRAS. Adobe Acrobat Reader is required to correctly display the (3D) animated figures (Fig. 9). Full data tables and supporting videos are also available at the BUDHIES project website: http://www.astro.rug.nl/budhies

Instability of the massive Klein-Gordon field on the Kerr spacetime

We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive Klein-Gordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the $l = 1$, $m = 1$ state, for $M \mu \lesssim 0.5$. For a fast rotating hole ($a = 0.99$) we find a maximum growth rate of $\tau^{-1} \approx 1.5 \times 10^{-7} (GM/c^3)^{-1}$, at $M \mu \approx 0.42$. The physical implications are discussed.Comment: Added references. 27 pages, 7 figure

BUDH IES V:The baryonic Tully-Fisher relation at z = 0.2 based on direct H I detections

We present H I-based B- and R-band Tully-Fisher relations (TFRs) and the Baryonic TFR (BTFR) at z = 0.2 using direct H I detections from the Blind Ultra-Deep H I Environmental Survey (BUDH IES). Deep photometry from the Isaac Newton Telescope was used for 36 out of 166 H I sources, matching the quality criteria required for a robust TFR analysis. Two velocity definitions at 20 and 50 per cent of the peak flux were measured from the global H I profiles and adopted as proxies for the circular velocities. We compare our results with an identically constructed z= 0 TFR from the Ursa Major association (UMa) of galaxies. To ensure an unbiased comparison of the TFR, all the samples were treated identically regarding sample selection and applied corrections. We provide catalogues and an atlas showcasing the properties of the galaxies. Our analysis is focused on the zero points of the TFR and BTFR with their slopes fixed to the z = 0 relation. Our main results are: (1) The BUDH IES galaxies show more asymmetric H I profiles with shallower wings compared to the UMa galaxies, which is likely due to the environment in which they reside, (2) The luminosity-based z= 0.2 TFRs are brighter and bluer than the z = 0 TFRs, even when cluster galaxies are excluded from the BUDH IES sample, (3) The BTFR shows no evolution in its zero point over the past 2.5 billion yr and does not significantly change on the inclusion of cluster galaxies, and (4) proper sample selection and consistent corrections are crucial for an unbiased analysis of the evolution of the TFR

From Heisenberg matrix mechanics to EBK quantization: theory and first applications

Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there are, nevertheless, a number of previously unexploited aspects of this relationship that bear on the quantum-classical correspondence. In particular, we emphasize a quantum variational principle that implies the classical variational principle for invariant tori. We also expose the more indirect connection between commutation relations and quantization of action variables. With the help of several standard models with one or two degrees of freedom, we then illustrate how the methods of Heisenberg matrix mechanics described in this paper may be used to obtain quantum solutions with a modest increase in effort compared to semiclassical calculations. We also describe and apply a method for obtaining leading quantum corrections to EBK results. Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.

BUDHIES II:A phase-space view of H I gas stripping and star formation quenching in cluster galaxies

We investigate the effect of ram-pressure from the intracluster medium on the stripping of H I gas in galaxies in a massive, relaxed, X-ray bright, galaxy cluster at z = 0.2 from the Blind Ultra Deep H I Environmental Survey (BUDHIES). We use cosmological simulations, and velocity versus position phase-space diagrams to infer the orbital histories of the cluster galaxies. In particular, we embed a simple analytical description of ram-pressure stripping in the simulations to identify the regions in phase-space where galaxies are more likely to have been sufficiently stripped of their H I gas to fall below the detection limit of our survey. We find a striking agreement between the model predictions and the observed location of H I-detected and non-detected blue (late-type) galaxies in phase-space, strongly implying that ram-pressure plays a key role in the gas removal from galaxies, and that this can happen during their first infall into the cluster. However, we also find a significant number of gas-poor, red (early-type) galaxies in the infall region of the cluster that cannot easily be explained with our model of ram-pressure stripping alone. We discuss different possible additional mechanisms that could be at play, including the pre-processing of galaxies in their previous environment. Our results are strengthened by the distribution of galaxy colours (optical and UV) in phase-space, that suggests that after a (gas-rich) field galaxy falls into the cluster, it will lose its gas via ram-pressure stripping, and as it settles into the cluster, its star formation will decay until it is completely quenched. Finally, this work demonstrates the utility of phase-space diagrams to analyse the physical processes driving the evolution of cluster galaxies, in particular H I gas stripping

Single polymer dynamics in elongational flow and the confluent Heun equation

We investigate the non-equilibrium dynamics of an isolated polymer in a stationary elongational flow. We compute the relaxation time to the steady-state configuration as a function of the Weissenberg number. A strong increase of the relaxation time is found around the coil-stretch transition, which is attributed to the large number of polymer configurations. The relaxation dynamics of the polymer is solved analytically in terms of a central two-point connection problem for the singly confluent Heun equation.Comment: 9 pages, 6 figure

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure