137 research outputs found

### Modelling Galaxies with f(E,Lz); a Black Hole in M32

A technique for the construction of axisymmetric distribution functions for
individual galaxies is presented. It starts from the observed surface bright-
ness distribution, which is deprojected to gain the axisymmetric luminosity
density, from which follows the stars' gravitational potential. After adding
dark mass components, such as a central black hole, the two-integral distribu-
tion function (2I-DF) f(E,Lz), which depends only on the classical integrals of
motion in an axisymmetric potential, is constructed using the Richardson- Lucy
algorithm. This algorithm proved to be very efficient in finding f(E,Lz)
provided the integral equation to be solved has been properly modified. Once
the 2I-\df\ is constructed, its kinematics can be computed and compared with
those observed. Many discrepancies may be remedied by altering the assumed
inclination angle, mass-to-light ratio, dark components, and odd part of the
2I-DF. Remaining discrepancies may indicate, that the distribution function
depends on the non-classical third integral, or is non-axisymmetric.
The method has been applied to the nearby elliptical galaxy M32. A 2I-DF with
~55 degrees inclination and a central black hole (or other compact dark mass
inside ~1pc) of 1.6-2*10^6 Msun fits the high-spatial-resolution kinema- tic
data of van der Marel et al. remarkably well. 2I-DFs with a significantly less
or more massive central dark mass or with edge-on inclination can be ruled out
for M32. Predictions are made for HST-observations: spectroscopy using its
smallest square aperture of 0.09"*0.09" should yield a non-gaussian central
velocity profile with broad wings, true and gaussian-fit velocity dispersion of
150-170km/s and 120-130km/s, respectively.Comment: 14 pages, 9 figures, uuencoded compressed ps file (468k), Ref:
OUTP-94-04

### A Very Fast and Momentum-Conserving Tree Code

The tree code for the approximate evaluation of gravitational forces is
extended and substantially accelerated by including mutual cell-cell
interactions. These are computed by a Taylor series in Cartesian coordinates
and in a completely symmetric fashion, such that Newton's third law is
satisfied by construction and hence momentum exactly conserved. The
computational effort is further reduced by exploiting the mutual symmetry of
the interactions. For typical astrophysical problems with N=10^5 and at the
same level of accuracy, the new code is about four times faster than the tree
code. For large N, the computational costs are found to scale almost linearly
with N, which can also be supported by a theoretical argument, and the
advantage over the tree code increases with ever larger N.Comment: revised version (accepted by ApJ Letters), 5 pages LaTeX, 3 figure

### A fast multipole method for stellar dynamics

The approximate computation of all gravitational forces between $N$
interacting particles via the fast multipole method (FMM) can be made as
accurate as direct summation, but requires less than $\mathcal{O}(N)$
operations. FMM groups particles into spatially bounded cells and uses
cell-cell interactions to approximate the force at any position within the sink
cell by a Taylor expansion obtained from the multipole expansion of the source
cell. By employing a novel estimate for the errors incurred in this process, I
minimise the computational effort required for a given accuracy and obtain a
well-behaved distribution of force errors. For relative force errors of
$\sim10^{-7}$, the computational costs exhibit an empirical scaling of $\propto
N^{0.87}$. My implementation (running on a 16 core node) out-performs a
GPU-based direct summation with comparable force errors for $N\gtrsim10^5$.Comment: 21 pages, 15 figures, accepted for publication in Journal for
Computational Astrophysics and Cosmolog

### Black hole foraging: feedback drives feeding

We suggest a new picture of supermassive black hole (SMBH) growth in galaxy
centers. Momentum-driven feedback from an accreting hole gives significant
orbital energy but little angular momentum to the surrounding gas. Once central
accretion drops, the feedback weakens and swept-up gas falls back towards the
SMBH on near-parabolic orbits. These intersect near the black hole with
partially opposed specific angular momenta, causing further infall and
ultimately the formation of a small-scale accretion disk. The feeding rates
into the disk typically exceed Eddington by factors of a few, growing the hole
on the Salpeter timescale and stimulating further feedback. Natural
consequences of this picture include (i) the formation and maintenance of a
roughly toroidal distribution of obscuring matter near the hole; (ii) random
orientations of successive accretion disk episodes; (iii) the possibility of
rapid SMBH growth; (iv) tidal disruption of stars and close binaries formed
from infalling gas, resulting in visible flares and ejection of hypervelocity
stars; (v) super-solar abundances of the matter accreting on to the SMBH; and
(vi) a lower central dark-matter density, and hence annihilation signal, than
adiabatic SMBH growth implies. We also suggest a simple sub-grid recipe for
implementing this process in numerical simulations.Comment: accepted for publication in ApJ Letters, 5 pages, 1 figur

### Dynamical Models for the Milky Way

The only way to map the Galaxy's gravitational potential $\Phi({\bf x})$ and
the distribution of matter that produces it is by modelling the dynamics of
stars and gas. Observations of the kinematics of gas provide key information
about gradients of $\Phi$ within the plane, but little information about the
structure of $\Phi$ out of the plane. Traditional Galaxy models {\em assume},
for each of the Galaxy's components, arbitrary flattenings, which together with
the components' relative masses yield the model's equipotentials. However, the
Galaxy's isopotential surfaces should be {\em determined\/} directly from the
motions of stars that move far from the plane. Moreover, from the kinematics of
samples of such stars that have well defined selection criteria, one should be
able not only to map $\Phi$ at all positions, but to determine the distribution
function $f_i({\bf x},{\bf v})$ of each stellar population $i$ studied. These
distribution functions will contain a wealth of information relevant to the
formation and evolution of the Galaxy. An approach to fitting a wide class of
dynamical models to the very heterogeneous body of available data is described
and illustrated.Comment: 10 pages, LaTeX, style file and 4 figures included. Invited talk
presented at the meeting ``Formation of the Galactic Halo ... Inside and
Out'', Tucson, October 9-11. Full .ps file available at
ftp://ftp.physics.ox.ac.uk/pub/local/users/dehnen/MilkyWayModels.ps.g

### Approximating Stellar Orbits: Improving on Epicycle Theory

Already slightly eccentric orbits, such as those occupied by many old stars
in the Galactic disk, are not well approximated by Lindblad's epicycle theory.
Here, alternative approximations for flat orbits in axisymmetric stellar
systems are derived and compared to results from numeric integrations. All of
these approximations are more accurate than Lindblad's classical theory. I also
present approximate, but canonical, maps from ordinary phase-space coordinates
to a set of action-angle variables.
Unfortunately, the most accurate orbit approximation leads to non-analytical
R(t). However, from this approximation simple and yet very accurate estimates
can be derived for the peri- and apo-centers, frequencies, and actions
integrals of galactic orbits, even for high eccentricities. Moreover, further
approximating this approximation allows for an analytical R(t) and still an
accurate approximation to galactic orbits, even with high eccentricities.Comment: accepted for publication in AJ; 12 pages LaTeX, 9 figures (coloured
only here, not in AJ) uses aas2pp4.st

### The outer rotation curve of the Milky Way

A straightforward determination of the circular-speed curve vc(R) of the
Milky Way suggests that near the Sun, vc starts to rise approximately linearly
with R. If this result were correct, the Galactic mass density would have to be
independent of radius at R ~> R0. We show that the apparent linear rise in v_c
arises naturally if the true circular-speed curve is about constant or gently
falling at R0 1.25 R0
are actually concentrated into a ring of radius ~1.6 R0.Comment: 3 pages, LaTeX, uses mn.sty, 5 .ps figures, submitted to MNRA

### Mass models of the Milky Way

A parameterized model of the mass distribution within the Milky Way is fitted
to the available observational constraints. The most important single parameter
is the ratio of the scale length R_d* of the stellar disk to R0. The disk and
bulge dominate v_c(R) at R<R0 only for R_d*/R0< 0.3. Since the only knowledge
we have of the halo derives from studies like the present one, we allow it to
contribute to the density at all radii. When allowed this freedom, however, the
halo causes changes in assumptions relating to R << R0 to affect profoundly the
structure of the best-fitting model at R >> R0. For example, changing the disk
slightly from an exponential surface-density profile significantly changes the
form of v_c(R) at R >> R0, where the disk makes a negligible contribution to
v_c. Moreover, minor changes in the constraints can cause the halo to develop a
deep hole at its centre that is not physically plausible. These problems call
into question the proposition that flat rotation curves arise because galaxies
have physically distinct halos rather than outwards-increasing mass-to-light
ratios.
The mass distribution of the Galaxy and the relative importance of its
various components will remain very uncertain until more observational data can
be used to constrain mass models. Data that constrain the Galactic force field
at z > R and at R > R0 are especially important.Comment: 10 pages, LaTeX, mn.sty, 5 .ps figures, accepted by MNRAS major
revision involving new cepheid & hipparcos dat

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