818 research outputs found
Hill's Equation with Random Forcing Parameters: The Limit of Delta Function Barriers
This paper considers random Hill's equations in the limit where the periodic
forcing function becomes a Dirac delta function. For this class of equations,
the forcing strength , the oscillation frequency \af_k, and the period
are allowed to vary from cycle to cycle. Such equations arise in astrophysical
orbital problems in extended mass distributions, in the reheating problem for
inflationary cosmologies, and in periodic Schr{\"o}dinger equations. The growth
rates for solutions to the periodic differential equation can be described by a
matrix transformation, where the matrix elements vary from cycle to cycle.
Working in the delta function limit, this paper addresses several coupled
issues: We find the growth rates for the matrices that describe
the solutions. This analysis is carried out in the limiting regimes of both
large and small forcing strength parameters. For the
latter case, we present an alternate treatment of the dynamics in terms of a
Fokker-Planck equation, which allows for a comparison of the two approaches.
Finally, we elucidate the relationship between the fundamental parameters
(\af_k,q_k) appearing in the stochastic differential equation and the matrix
elements that specify the corresponding discrete map. This work provides
analytic -- and accurate -- expressions for the growth rates of these
stochastic differential equations in both the and the
limits.Comment: 29 pages, 3 figures, accepted to Journal of Mathematical Physic
The Effect of the Outer Lindblad Resonance of the Galactic Bar on the Local Stellar Velocity Distribution
Hydro-dynamical modeling of the inner Galaxy suggest that the radius of the
outer Lindblad resonance (OLR) of the Galactic bar lies in the vicinity of the
Sun. How does this resonance affect the distribution function in the outer
parts of a barred disk, and can we identify any effect of the resonance in the
velocity distribution f(v) actually observed in the solar neighborhood? To
answer these questions, detailed simulations of f(v) in the outer parts of an
exponential stellar disks with nearly flat rotation curves and a rotating
central bar have been performed. For a model resembling the old stellar disk,
the OLR causes a distinct feature in f(v) over a significant fraction of the
outer disk. For positions <2kpc outside the OLR radius and at bar angles of
\~10-70 degrees, f(v) inhibits a bi-modality between the low-velocity stars
moving like the local standard of rest (LSR) and a secondary mode of stars
predominantly moving outward and rotating more slowly than the LSR.
Such a bi-modality is indeed present in f(v) inferred from the Hipparcos data
for late-type stars in the solar neighborhood. If one interpretes this observed
bi-modality as induced by the OLR -- and there are hardly any viable
alternatives -- then one is forced to deduce that the OLR radius is slightly
smaller than Ro. Moreover, by a quantitative comparison of the observed with
the simulated distributions one finds that the pattern speed of the bar is
1.85+/-0.15 times the local circular frequency, where the error is dominated by
the uncertainty in bar angle and local circular speed.
Also other, less prominent but still significant, features in the observed
f(v) resemble properties of the simulated velocity distributions, in particular
a ripple caused by orbits trapped in the outer 1:1 resonance.Comment: 14 pages, 10 figures (Fig.2 in full resolution available upon
request), accepted for publication in A
Tidally Compressed Gas in Centers of Early Type and Ultraluminous Galaxies
In this paper we propose that the compressive tidal field in the centers of
flat-core early type galaxies and ultraluminous galaxies compresses molecular
clouds producing dense gas obseved in the centers of these galaxies. The effect
of galactic tidal fields is usually considered disruptive in the literature.
However, for some galaxies, the mass profile flattens towards the center and
the resulting galactic tidal field is not disruptive but instead it is
compressive within the flat-core region. We have used the virial theorem to
determine the minimum density of a molecular cloud to be stable and
gravitationally bound within the tidally compressive region of a galaxy. We
have applied the mechanism to determine the mean molecular cloud densities in
the centers of a sample of flat-core, early-type galaxies and ultraluminous
galaxies.Comment: 18 latex pages and uses aaspp4.sty, accepted for publication in
Astrophysical Journa
Milky Way Mass Models and MOND
Using the Tuorla-Heidelberg model for the mass distribution of the Milky Way,
I determine the rotation curve predicted by MOND. The result is in good
agreement with the observed terminal velocities interior to the solar radius
and with estimates of the Galaxy's rotation curve exterior thereto. There are
no fit parameters: given the mass distribution, MOND provides a good match to
the rotation curve. The Tuorla-Heidelberg model does allow for a variety of
exponential scale lengths; MOND prefers short scale lengths in the range 2.0 to
2.5 kpc. The favored value of scale length depends somewhat on the choice of
interpolation function. There is some preference for the `simple' interpolation
function as found by Famaey & Binney. I introduce an interpolation function
that shares the advantages of the simple function on galaxy scales while having
a much smaller impact in the solar system. I also solve the inverse problem,
inferring the surface mass density distribution of the Milky Way from the
terminal velocities. The result is a Galaxy with `bumps and wiggles' in both
its luminosity profile and rotation curve that are reminiscent of those
frequently observed in external galaxies.Comment: Accepted for publication in the Astrophysical Journal. 31 pages
including 8 figures and 3 table
Triaxial orbit based galaxy models with an application to the (apparent) decoupled core galaxy NGC 4365
We present a flexible and efficient method to construct triaxial dynamical
models of galaxies with a central black hole, using Schwarzschild's orbital
superposition approach. Our method is general and can deal with realistic
luminosity distributions, which project to surface brightness distributions
that may show position angle twists and ellipticity variations. The models are
fit to measurements of the full line-of-sight velocity distribution (wherever
available). We verify that our method is able to reproduce theoretical
predictions of a three-integral triaxial Abel model. In a companion paper (van
de Ven, de Zeeuw & van den Bosch), we demonstrate that the method recovers the
phase-space distribution function. We apply our method to two-dimensional
observations of the E3 galaxy NGC 4365, obtained with the integral-field
spectrograph SAURON, and study its internal structure, showing that the
observed kinematically decoupled core is not physically distinct from the main
body and the inner region is close to oblate axisymmetric.Comment: 21 Pages, 14 (Colour) Figures, Companion paper is arXiv:0712.0309
Accepted to MNRAS. Full resolution version at
http://www.strw.leidenuniv.nl/~bosch/papers/RvdBosch_triaxmethod.pd
Cosmological Parameters from Observations of Galaxy Clusters
Studies of galaxy clusters have proved crucial in helping to establish the
standard model of cosmology, with a universe dominated by dark matter and dark
energy. A theoretical basis that describes clusters as massive,
multi-component, quasi-equilibrium systems is growing in its capability to
interpret multi-wavelength observations of expanding scope and sensitivity. We
review current cosmological results, including contributions to fundamental
physics, obtained from observations of galaxy clusters. These results are
consistent with and complementary to those from other methods. We highlight
several areas of opportunity for the next few years, and emphasize the need for
accurate modeling of survey selection and sources of systematic error.
Capitalizing on these opportunities will require a multi-wavelength approach
and the application of rigorous statistical frameworks, utilizing the combined
strengths of observers, simulators and theorists.Comment: 53 pages, 21 figures. To appear in Annual Review of Astronomy &
Astrophysic
Halo Geometry and Dark Matter Annihilation Signal
We study the impact of the halo shape and geometry on the expected weakly
interacting massive particle (WIMP) dark matter annihilation signal from the
galactic center. As the halo profile in the innermost region is still poorly
constrained, we consider different density behaviors like flat cores, cusps and
spikes, as well as geometrical distortions. We show that asphericity has a
strong impact on the annihilation signal when the halo profile near the
galactic center is flat, but becomes gradually less significant for cuspy
profiles, and negligible in the presence of a central spike. However, the
astrophysical factor is strongly dependent on the WIMP mass and annihilation
cross-section in the latter case.Comment: 5 pages, 4 figures, PR
The properties of the Galactic bar implied by gas kinematics in the inner Milky Way
Longitude-velocity (l-V) diagrams of H I and CO gas in the inner Milky Way
have long been known to be inconsistent with circular motion in an axisymmetric
potential. Several lines of evidence suggest that the Galaxy is barred, and gas
flow in a barred potential could be consistent with the observed ``forbidden''
velocities and other features in the data. We compare the H I observations to
l-V diagrams synthesized from 2-D fluid dynamical simulations of gas flows in a
family of barred potentials. The gas flow pattern is very sensitive to the
parameters of the assumed potential, which allows us to discriminate among
models. We present a model that reproduces the outer contour of the H I l-V
diagram reasonably well; this model has a strong bar with a semimajor axis of
3.6 kpc, an axis ratio of approximately 3:1, an inner Lindblad resonance (ILR),
and a pattern speed of 42 km/s/kpc, and matches the data best when viewed from
34\deg to the bar major axis. The behavior of the models, combined with the
constraint that the shocks in the Milky Way bar should resemble those in
external barred galaxies, leads us to conclude that wide ranges of parameter
space are incompatible with the observations. In particular we suggest that the
bar must be fairly strong, must have an ILR, and cannot be too end-on, with the
bar major axis at 35\deg +/- 5\deg to the line of sight. The H I data exhibit
larger forbidden velocities over a wider longitude range than are seen in
molecular gas; this important difference is the reason our favored model
differs so significantly from other recently proposed models.Comment: 23 pages, 14 figures, 1 table, uses emulateapj and psfig, 640 kb.
Submitted to Ap
Non-linear Evolution of f(R) Cosmologies III: Halo Statistics
The statistical properties of dark matter halos, the building blocks of
cosmological observables associated with structure in the universe, offer many
opportunities to test models for cosmic acceleration, especially those that
seek to modify gravitational forces. We study the abundance, bias and profiles
of halos in cosmological simulations for one such model: the modified action
f(R) theory. In the large field regime that is accessible to current
observations, enhanced gravitational forces raise the abundance of rare massive
halos and decrease their bias but leave their (lensing) mass profiles largely
unchanged. This regime is well described by scaling relations based on a
modification of spherical collapse calculations. In the small field regime,
enhanced forces are suppressed inside halos and the effects on halo properties
are substantially reduced for the most massive halos. Nonetheless, the scaling
relations still retain limited applicability for the purpose of establishing
conservative upper limits on the modification to gravity.Comment: 12 pages, 10 figures; v2: revised version accepted by Phys. Rev.
SPH Simulations of Galactic Gaseous Disk with Bar: Distribution and Kinematic Structure of Molecular Clouds toward the Galactic Center
We have performed Smoothed Particle Hydrodynamic (SPH) simulations to study
the response of molecular clouds in the Galactic disk to a rotating bar and
their subsequent evolution in the Galactic Center (GC) region. The Galactic
potential in our models is contributed by three axisymmetric components
(massive halo, exponential disk, compact bulge) and a non-axisymmetric bar.
These components are assumed to be invariant in time in the frame corotating
with the bar. Some noticeable features such as an elliptical outer ring, spiral
arms, a gas-depletion region, and a central concentration have been developed
due to the influence of the bar. The rotating bar induces non-circular motions
of the SPH particles, but hydrodynamic collisions tend to suppress the random
components of the velocity. The velocity field of the SPH particles is
consistent with the kinematics of molecular clouds observed in HCN (1-0)
transition; these clouds are thought to be very dense clouds. However, the l-v
diagram of the clouds traced by CO is quite different from that of our SPH
simulation, being more similar to that obtained from simulations using
collisionless particles. The diagram of a mixture of collisional and
collisionless particles gives better reproduction of the kinematic structures
of the GC clouds observed in the CO line. The fact that the kinematics of HCN
clouds can be reproduced by the SPH particles suggests that the dense clouds in
the GC are formed via cloud collisions induced by rotating bar.Comment: 31 pages, 10 pigures, accepted for publication in Ap
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