1,442 research outputs found
Orbit-superposition models of discrete, incomplete stellar kinematics: application to the Galactic centre
We present a method for fitting orbit-superposition models to the kinematics
of discrete stellar systems when the available stellar sample has been filtered
by a known selection function. The fitting method can be applied to any model
in which the distribution function is represented as a linear superposition of
basis elements with unknown weights. As an example, we apply it to Fritz et
al.'s kinematics of the innermost regions of the Milky Way's nuclear stellar
cluster. Assuming spherical symmetry, our models fit a black hole of mass
, surrounded by an extended mass
within 4 pc. Within 1 pc the
best-fitting mass models have an approximate power-law density cusp
with . We carry out an extensive
investigation of how our modelling assumptions might bias these estimates:
is the most robust parameter and the least. Internally the
best-fitting models have broadly isotropic orbit distributions, apart from a
bias towards circular orbits between 0.1 and 0.3 parsec.Comment: 17 pages, MNRAS accepte
Kinematical signatures of hidden stellar discs
The deprojection of the surface brightness distribution of an axisymmetric
galaxy does not have a unique solution unless the galaxy is viewed precisely
edge-on. I present an algorithm that finds the full range of smooth
axisymmetric density distributions consistent with a given surface brightness
distribution and inclination angle, and use it to investigate the effects of
this non-uniqueness on the line-of-sight velocity profiles (VPs) of
two-integral models of both real and toy disky galaxies viewed at a range of
inclination angles. Photometrically invisible face-on disks leave very clear
signatures in the minor-axis VPs of the models (Gauss--Hermite coefficients
h_4>0.1), provided the disk-to-bulge ratio is greater than about 3%. I discuss
the implications of these hitherto neglected disks for dynamical modelling.Comment: 7 pages, 7 figures, uses mn.te
Constraining black hole masses from stellar kinematics by summing over all possible distribution functions
When faced with the task of constraining a galaxy's potential given limited
stellar kinematical information, what is the best way of treating the galaxy's
unknown distribution function (DF)? Using the example of estimating black hole
(BH) masses, I argue that the correct approach is to consider all possible DFs
for each trial potential, marginalizing the DF using an infinitely divisible
prior. Alternative approaches, such as the widely used maximum penalized
likelihood method, neglect the huge degeneracies inherent in the problem and
simply identify a single, special DF for each trial potential.
Using simulated observations of toy galaxies with realistic amounts of noise,
I find that this marginalization procedure yields significantly tighter
constraints on BH masses than the conventional maximum-likelihood method,
although it does pose a computational challenge which might be solved with the
development of a suitable algorithm for massively parallel machines. I show
that in practice the conventional maximum-likelihood method yields reliable BH
masses with well-defined minima in their chi^2 distributions, contrary to
claims made by Valluri, Merritt & Emsellem.Comment: 11 pages, 7 figures, 1 tabl
Rates of tidal disruption of stars by massive central black holes
There is strong evidence for some kind of massive dark object in the centres
of many galaxy bulges. The detection of flares from tidally disrupted stars
could confirm that these objects are black holes (BHs). Here we present
calculations of the stellar disruption rates in detailed dynamical models of
real galaxies, taking into account the refilling of the loss cone of stars on
disruptable orbits by two-body relaxation and tidal forces in non-spherical
galaxies. The highest disruption rates (one star per 10^4 yr) occur in faint
(L>10^10 L_sun) galaxies, which have steep central density cusps. More luminous
galaxies are less dense and have much longer relaxation times and more massive
BHs. Dwarf stars in such galaxies are swallowed whole by the BH and hence do
not emit flares; giant stars could produce flares as often as every 10^5 yr,
although the rate depends sensitively on the shape of the stellar distribution
function. We discuss the possibility of detecting disruption flares in current
supernova searches. The total mass of stars consumed over the lifetime of the
galaxy is of order 10^6 M_sun, independent of galaxy luminosity; thus disrupted
stars may contribute significantly to the present BH mass in galaxies fainter
than about 10^9 L_sun.Comment: 14 pages, 5 figures, 1 landscape table. Submitted to MNRA
Three-dimensional extinction mapping using Gaussian random fields
We present a scheme for using stellar catalogues to map the three-dimensional
distributions of extinction and dust within our Galaxy. Extinction is modelled
as a Gaussian random field, whose covariance function is set by a simple
physical model of the ISM that assumes a Kolmogorov-like power spectrum of
turbulent fluctuations. As extinction is modelled as a random field, the
spatial resolution of the resulting maps is set naturally by the data
available; there is no need to impose any spatial binning. We verify the
validity of our scheme by testing it on simulated extinction fields and show
that its precision is significantly improved over previous dust-mapping
efforts. The approach we describe here can make use of any photometric,
spectroscopic or astrometric data; it is not limited to any particular survey.
Consequently, it can be applied to a wide range of data from both existing and
future surveys.Comment: 16 pages, 12 figures. Submitted for publication in MNRAS. Text
revise
Recognizing the fingerprints of the Galactic bar: a quantitative approach to comparing model (l,v) distributions to observation
We present a new method for fitting simple hydrodynamical models to the (l,v)
distribution of atomic and molecular gas observed in the Milky Way. The method
works by matching features found in models and observations. It is based on the
assumption that the large-scale features seen in (l,v) plots, such as
ridgelines and the terminal velocity curve, are influenced primarily by the
underlying large-scale Galactic potential and are only weakly dependent on
local ISM heating and cooling processes. In our scheme one first identifies by
hand the features in the observations: this only has to be done once. We
describe a procedure for automatically extracting similar features from simple
hydrodynamical models and quantifying the "distance" between each model's
features and the observations. Application to models of the Galactic Bar region
(|l|<30deg) shows that our feature-fitting method performs better than \chi^2
or envelope distances at identifying the correct underlying galaxy model.Comment: Accepted for publication in MNRA
The secular evolution of discrete quasi-Keplerian systems. I. Kinetic theory of stellar clusters near black holes
We derive the kinetic equation that describes the secular evolution of a
large set of particles orbiting a dominant massive object, such as stars bound
to a supermassive black hole or a proto-planetary debris disc encircling a
star. Because the particles move in a quasi-Keplerian potential, their orbits
can be approximated by ellipses whose orientations remain fixed over many
dynamical times. The kinetic equation is obtained by simply averaging the BBGKY
equations over the fast angle that describes motion along these ellipses. This
so-called Balescu-Lenard equation describes self-consistently the long-term
evolution of the distribution of quasi-Keplerian orbits around the central
object: it models the diffusion and drift of their actions, induced through
their mutual resonant interaction. Hence, it is the master equation that
describes the secular effects of resonant relaxation. We show how it captures
the phenonema of mass segregation and of the relativistic Schwarzschild barrier
recently discovered in -body simulations.Comment: 24 pages, 3 figure
Gas flow in barred potentials
We use a Cartesian grid to simulate the flow of gas in a barred Galactic
potential and investigate the effects of varying the sound speed in the gas and
the resolution of the grid. For all sound speeds and resolutions, streamlines
closely follow closed orbits at large and small radii. At intermediate radii
shocks arise and the streamlines shift between two families of closed orbits.
The point at which the shocks appear and the streamlines shift between orbit
families depends strongly on sound speed and resolution. For sufficiently large
values of these two parameters, the transfer happens at the cusped orbit as
hypothesised by Binney et al. over two decades ago. For sufficiently high
resolutions the flow downstream of the shocks becomes unsteady. If this
unsteadiness is physical, as appears to be the case, it provides a promising
explanation for the asymmetry in the observed distribution of CO.Comment: Accepted for publication in MNRA
Gas flow in barred potentials II. Bar Driven Spiral Arms
Spiral arms that emerge from the ends of a galactic bar are important in
interpreting observations of our and external galaxies. It is therefore
important to understand the physical mechanism that causes them. We find that
these spiral arms can be understood as kinematic density waves generated by
librations around underlying ballistic closed orbits. This is even true in the
case of a strong bar, provided the librations are around the appropriate closed
orbits and not around the circular orbits that form the basis of the epicycle
approximation. An important consequence is that it is a potential's orbital
structure that determines whether a bar should be classified as weak or strong,
and not crude estimates of the potential's deviation from axisymmetry.Comment: Accepted for publication in MNRA
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