On the stability of plane Couette-Poiseuille flow with uniform cross-flow

We present a detailed study of the linear stability of plane Couette-Poiseuille flow in the presence of a cross-flow. The base flow is characterised by the cross flow Reynolds number, $R_{inj}$ and the dimensionless wall velocity, $k$. Squire's transformation may be applied to the linear stability equations and we therefore consider 2D (spanwise-independent) perturbations. Corresponding to each dimensionless wall velocity, $k\in[0,1]$, two ranges of $R_{inj}$ exist where unconditional stability is observed. In the lower range of $R_{inj}$, for modest $k$ we have a stabilisation of long wavelengths leading to a cut-off $R_{inj}$. This lower cut-off results from skewing of the velocity profile away from a Poiseuille profile, shifting of the critical layers and the gradual decrease of energy production. Cross-flow stabilisation and Couette stabilisation appear to act via very similar mechanisms in this range, leading to the potential for robust compensatory design of flow stabilisation using either mechanism. As $R_{inj}$ is increased, we see first destabilisation and then stabilisation at very large $R_{inj}$. The instability is again a long wavelength mechanism. Analysis of the eigenspectrum suggests the cause of instability is due to resonant interactions of Tollmien-Schlichting waves. A linear energy analysis reveals that in this range the Reynolds stress becomes amplified, the critical layer is irrelevant and viscous dissipation is completely dominated by the energy production/negation, which approximately balances at criticality. The stabilisation at very large $R_{inj}$ appears to be due to decay in energy production, which diminishes like $R_{inj}^{-1}$. Our study is limited to two dimensional, spanwise independent perturbations.Comment: Accepted for publication in Journal of Fluid Mechanic

Secular Evolution of Galaxy Morphologies

Today we have numerous evidences that spirals evolve dynamically through various secular or episodic processes, such as bar formation and destruction, bulge growth and mergers, sometimes over much shorter periods than the standard galaxy age of 10-15 Gyr. This, coupled to the known properties of the Hubble sequence, leads to a unique sense of evolution: from Sm to Sa. Linking this to the known mass components provides new indications on the nature of dark matter in galaxies. The existence of large amounts of yet undetected dark gas appears as the most natural option. Bounds on the amount of dark stars can be given since their formation is mostly irreversible and requires obviously a same amount of gas.Comment: 8 pages, Latex2e, crckapb.sty macros, 1 Postscript figure, replaced with TeX source; To be published in the proceeedings of the "Dust-Morphology" conference, Johannesburg, 22-26 January, 1996, D. Block (ed.), (Kluwer Dordrecht

The Destruction of Bars by Central Mass Concentrations

More than two thirds of disk galaxies are barred to some degree. Many today harbor massive concentrations of gas in their centers, and some are known to possess supermassive black holes (SMBHs) and their associated stellar cusps. Previous theoretical work has suggested that a bar in a galaxy could be dissolved by the formation of a mass concentration in the center, although the precise mass and degree of central concentration required is not well-established. We report an extensive study of the effects of central masses on bars in high-quality N-body simulations of galaxies. We have varied the growth rate of the central mass, its final mass and degree of concentration to examine how these factors affect the evolution of the bar. Our main conclusions are: (1) Bars are more robust than previously thought. The central mass has to be as large as several percent of the disk mass to completely destroy the bar on a short timescale. (2) For a given mass, dense objects cause the greatest reduction in bar amplitude, while significantly more diffuse objects have a lesser effect. (3) The bar amplitude always decreases as the central mass is grown, and continues to decay thereafter on a cosmological time-scale. (4) The first phase of bar-weakening is due to the destruction by the CMC of lower-energy, bar-supporting orbits, while the second phase is a consequence of secular changes to the global potential which further diminish the number of bar-supporting orbits. We provide detailed phase-space and orbit analysis to support this suggestion. Thus current masses of SMBHs are probably too small, even when dressed with a stellar cusp, to affect the bar in their host galaxies. The molecular gas concentrations found in some barred galaxies are also too diffuse to affect the amplitude of the bar significantly.Comment: AASTeX v5.0 preprint; 44 pages, including 1 table and 16 figures. To appear in ApJ. High resolution version can be found at http://www.physics.rutgers.edu/~shen/bar_destruct/paper_high_res.pd

The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation

We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known as Hamiltonian Hopf Bifurcation) the four eigenvalues of the stable periodic orbits move out of the unit circle. Then the periodic orbits become complex unstable. In this paper we first integrate initial conditions close to the ones of a complex unstable periodic orbit, which is close to the transition point. Then, we plot the consequents of the corresponding orbit in a 4D surface of section. To visualize this surface of section we use the method of color and rotation [Patsis and Zachilas 1994]. We find that the consequents are contained in 2D "confined tori". Then, we investigate the structure of the phase space in the neighborhood of complex unstable periodic orbits, which are further away from the transition point. In these cases we observe clouds of points in the 4D surfaces of section. The transition between the two types of orbital behavior is abrupt.Comment: 10 pages, 14 figures, accepted for publication in the International Journal of Bifurcation and Chao

Why Buckling Stellar Bars Weaken in Disk Galaxies

Young stellar bars in disk galaxies experience a vertical buckling instability which terminates their growth and thickens them, resulting in a characteristic peanut/boxy shape when viewed edge on. Using N-body simulations of galactic disks embedded in live halos, we have analyzed the bar structure throughout this instability and found that the outer third of the bar dissolves completely while the inner part (within the vertical inner Lindblad resonance) becomes less oval. The bar acquires the frequently observed peanut/boxy-shaped isophotes. We also find that the bar buckling is responsible for a mass injection above the plane, which is subsequently trapped by specific 3-D families of periodic orbits of particular shapes explaining the observed isophotes, in line with previous work. Using a 3-D orbit analysis and surfaces of sections, we infer that the outer part of the bar is dissolved by a rapidly widening stochastic region around its corotation radius -- a process related to the bar growth. This leads to a dramatic decrease in the bar size, decrease in the overall bar strength and a mild increase in its pattern speed, but is not expected to lead to a complete bar dissolution. The buckling instability appears primarily responsible for shortening the secular diffusion timescale to a dynamical one when building the boxy isophotes. The sufficiently long timescale of described evolution, ~1 Gyr, can affect the observed bar fraction in local universe and at higher redshifts, both through reduced bar strength and the absence of dust offset lanes in the bar.Comment: 7 pages, 4 figures, ApJ Letters, in pres

Probing For Machos of Mass 10−15M⊙10^{-15}M_\odot-10−7M⊙10^{-7}M_\odot with Gamma-Ray Burst Parallax Spacecraft

Two spacecraft separated by \sim 1\,\au and equipped with gamma-ray burst (GRB) detectors could detect or rule out a cosmological density of Massive Compact Halo Objects (MACHOs) in the mass range 10^{-15} M_{\odot}\lsim M \lsim 10^{-7} M_{\odot} provided that GRBs prove to be cosmological. Previously devised methods for detecting MACHOs have spanned the mass range 10^{-16} M_{\odot}\lsim M \lsim 10^{7} M_{\odot}, but with a gap of several orders of magnitude near $10^{-9} M_{\odot}$. For MACHOs and sources both at a cosmological distance, the Einstein radius is \sim 1\,\au\,(M/10^{-7} M_\odot)^{1/2}. Hence, if a GRB lies within the Einstein ring of a MACHO of mass M\lsim 10^{-7}M_\odot as seen by one detector, it will not lie in the Einstein ring as seen by a second detector \sim 1\,\au away. This implies that if GRBs are measured to have significantly different fluxes by the two detectors, this would signal the presence of a MACHO \lsim 10^{-7}M_\odot. By the same token, if the two detectors measured similar fluxes for several hundred events a cosmological abundance of such low-mass MACHOs would be ruled out. The lower limit of sensitivity, M\lsim 10^{-15}M_\odot is set by the finite size of the source. If low-mass MACHOs are detected, there are tests which can discriminate among events generated by MACHOs in the three mass ranges M\lsim 10^{-12}\,M_\odot, 10^{-12}\,M_\odot\lsim M\lsim 10^{-7}\,M_\odot, and M\gsim 10^{-7}\ M_\odot. Further experiments would then be required to make more accurate mass measurements.Comment: 8 pages, uuencoded postscript, no figure

The structure of invariant tori in a 3D galactic potential

We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the 4D spaces of section. We compare our results with those of previous works and we describe the morphology of the rotational, as well as of the tube tori in the 4D space. We find sticky chaotic orbits in the immediate neighborhood of sets of invariant tori surrounding 3D stable periodic orbits. Particularly useful for galactic dynamics is the behavior of chaotic orbits trapped for long time between 4D invariant tori. We find that they support during this time the same structure as the quasi-periodic orbits around the stable periodic orbits, contributing however to a local increase of the dispersion of velocities. Finally we find that the tube tori do not appear in the 3D projections of the spaces of section in the axisymmetric Hamiltonian we examined.Comment: 26 pages, 34 figures, accepted for publication in the International Journal of Bifurcation and Chao

Self-consistent models of cuspy triaxial galaxies with dark matter haloes

We have constructed realistic, self-consistent models of triaxial elliptical galaxies embedded in triaxial dark matter haloes. We examined three different models for the shape of the dark matter halo: (i) the same axis ratios as the luminous matter (0.7:0.86:1); (ii) a more prolate shape (0.5:0.66:1); (iii) a more oblate shape (0.7:0.93:1). The models were obtained by means of the standard orbital superposition technique introduced by Schwarzschild. Self-consistent solutions were found in each of the three cases. Chaotic orbits were found to be important in all of the models,and their presence was shown to imply a possible slow evolution of the shapes of the haloes. Our results demonstrate for the first time that triaxial dark matter haloes can co-exist with triaxial galaxies.Comment: Latex paper based on the AASTEX format, 20 pages, 11 figures, 2 tables. Paper submitted to Ap

Dynamical Evolution of Elliptical Galaxies with Central Singularities

We study the effect of a massive central singularity on the structure of a triaxial galaxy using N-body simulations. Starting from a single initial model, we grow black holes with various final masses Mh and at various rates, ranging from impulsive to adiabatic. In all cases, the galaxy achieves a final shape that is nearly spherical at the center and close to axisymmetric throughout. However, the rate of change of the galaxy's shape depends strongly on the ratio Mh/Mg of black hole mass to galaxy mass. When Mh/Mg < 0.3%, the galaxy evolves in shape on a timescale that exceeds 100 orbital periods, or roughly a galaxy lifetime. When Mh/Mg > 2%, the galaxy becomes axisymmetric in little more than a crossing time. We propose that the rapid evolution toward axisymmetric shapes that occurs when Mh/Mg > 2% provides a negative feedback mechanism which limits the mass of central black holes by cutting off their supply of fuel.Comment: 27 Latex pages, 9 Postscript figures, uses aastex.sty. Accepted for Publication in The Astrophysical Journal, Nov. 26, 199

A Search for Stellar Obscuration Events due to Dark Clouds

The recent detections of a large population of faint submillimetre sources, an excess halo gamma-ray background, and the extreme scattering events observed for extragalactic radio sources have been explained as being due to baryonic dark matter in the form of small, dark, gas clouds. In this paper we present the results of a search for the transient stellar obscurations such clouds are expected to cause. We examine the Macho project light curves of 48 x 10^6 stars toward the Galactic bulge, LMC and SMC for the presence of dark cloud extinction events. We find no evidence for the existence of a population of dark gas clouds with Av > 0.2 and masses between ~ 10^-4 and 10^-2 M_solar in the Galactic disk or halo. However, it is possible that such dark cloud populations could exist if they are clustered in regions away from the observed lines of sight.Comment: 13 pages, 9 figures, submitted to Ap