298 research outputs found
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, and the
dimensionless wall velocity, . 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, ,
two ranges of exist where unconditional stability is observed. In the
lower range of , for modest we have a stabilisation of long
wavelengths leading to a cut-off . 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 is increased,
we see first destabilisation and then stabilisation at very large .
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 appears to be due to decay in energy
production, which diminishes like . 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 - 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 . 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
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