205 research outputs found

### Cartography for Martian Trojans

The last few months have seen the discovery of a second Martian Trojan (1998
VF31), as well as two further possible candidates (1998 QH56 and 1998 SD4).
Together with the previously discovered Martian satellite 5261 Eureka, these
are the only known possible solar system Trojan asteroids not associated with
Jupiter. Here, maps of the locations of the stable Trojan trajectories of Mars
are presented. These are constructed by integrating an ensemble of in-plane and
inclined orbits in the vicinity of the Martian Lagrange points for between 25
million and 60 million years. The survivors occupy a band of inclinations
between 15 degrees and 40 degrees and longitudes between 240 degrees and 330
degrees at the L5 Lagrange point. Around the L4 point, stable Trojans inhabit
two bands of inclinations (15 degrees < i < 30 degrees and 32 degrees < i < 40
degrees) with longitudes restricted between 25 degrees and 120 degrees. Both
5261 Eureka and 1998 VF31 lie deep within one of the stable zones, which
suggests they may be of primordial origin. Around Mars, the number of such
undiscovered primordial objects with sizes greater than 1 km may be as high as
50. The two candidates 1998 QH56 and 1998 SD4 are not presently on Trojan
orbits and will enter the sphere of influence of Mars within half a million
years.Comment: 14 pages, 3 figures, in press at the Astrophysical Journal (Letters

### The Capture of Centaurs as Trojans

Large scale simulations of Centaurs have yielded vast amounts of data, the
analysis of which allows interesting but uncommon scenarios to be studied. One
such rare phenomenon is the temporary capture of Centaurs as Trojans of the
giant planets. Such captures are generally short (10 kyr to 100 kyr), but occur
with sufficient frequency (about 40 objects larger than 1 km in diameter every
Myr) that they may well contribute to the present-day populations. Uranus and
Neptune seem to have great difficulty capturing Centaurs into the 1:1
resonance, while Jupiter captures some, and Saturn the most (80 %). We
conjecture that such temporary capture from the Centaur population may be the
dominant delivery route into the Saturnian Trojans. Photometric studies of the
Jovian Trojans may reveal outliers with Centaur-like as opposed to asteroidal
characteristics, and these would be prime candidates for captured Centaurs.Comment: 5 pages, 2 figures, submitted to MNRAS (Letters

### Linear multistep methods for integrating reversible differential equations

This paper studies multistep methods for the integration of reversible
dynamical systems, with particular emphasis on the planar Kepler problem. It
has previously been shown by Cano & Sanz-Serna that reversible linear
multisteps for first-order differential equations are generally unstable. Here,
we report on a subset of these methods -- the zero-growth methods -- that evade
these instabilities. We provide an algorithm for identifying these rare
methods. We find and study all zero-growth, reversible multisteps with six or
fewer steps. This select group includes two well-known second-order multisteps
(the trapezoidal and explicit midpoint methods), as well as three new
fourth-order multisteps -- one of which is explicit. Variable timesteps can be
readily implemented without spoiling the reversibility. Tests on Keplerian
orbits show that these new reversible multisteps work well on orbits with low
or moderate eccentricity, although at least 100 steps/radian are required for
stability.Comment: 31 pages, 9 figures, in press at The Astronomical Journa

### Comptonisation of Cosmic Microwave Background Photons in Dwarf Spheroidal Galaxies

We present theoretical modelling of the electron distribution produced by
annihilating neutralino dark matter in dwarf spheroidal galaxies (dSphs). In
particular, we follow up the idea of Colafrancesco (2004) and find that such
electrons distort the cosmic microwave background (CMB) by the
Sunyaev-Zeldovich effect. For an assumed neutralino mass of 10 GeV and beam
size of 1'', the SZ temperature decrement is of the order of nano-Kelvin for
dSph models with a soft core. By contrast, it is of the order of micro-Kelvin
for the strongly cusped dSph models favoured by some cosmological simulations.
Although this is out of reach of current instruments, it may well be detectable
by future mm telescopes, such as ALMA. We also show that the upscattered CMB
photons have energies within reach of upcoming X-ray observatories, but that
the flux of such photons is too small to be detectable soon. Nonetheless, we
conclude that searching for the dark matter induced Sunyaev-Zeldovich effect is
a promising way of constraining the dark distribution in dSphs, especially if
the particles are light.Comment: 10 pages, 5 figures, MNRAS, in pres

### Microlensing Halo Models with Abundant Brown Dwarfs

All previous attempts to understand the microlensing results towards the
Large Magellanic Cloud (LMC) have assumed homogeneous present day mass
functions (PDMFs) for the lensing populations. Here, we present an
investigation into the microlensing characteristics of haloes with spatially
varying PDMFs and anisotropic velocity dispersion tensors. One attractive
possibility -- suggested by baryonic dark cluster formation in pregalactic and
protogalactic cooling flows -- is that the inner halo is dominated by stellar
mass objects, whereas low mass brown dwarfs become more prevalent on moving
outwards. The contribution to the microlensing rate must be dominated by dark
remnants (of about 0.5 solar masses) to recover the observed timescales of the
microlensing experiments. But, even though stellar remnants control the rate,
they do not dominate the mass of the baryonic halo, and so the well-known
enrichment and mass budget problems are much less severe. Using a simple ansatz
for the spatial variation of the PDMF, models are constructed in which the
contribution of brown dwarfs to the mass of the baryonic halo is 55 % and to
the total halo is 30 %. An unusual property of the models is that they predict
that the average timescale of events towards M31 is shorter than the average
timescale towards the LMC. This is because the longer line of sight towards M31
probes more of the far halo where brown dwarfs are the most common constituent.Comment: 17 pages, 1 figure, in press at The Astrophysical Journal (Letters

### A Dynamical Model of the Inner Galaxy

An extension of Schwarzschild's galaxy-building technique is presented that,
for the first time, enables one to build Schwarzschild models with known
distribution functions (DFs). The new extension makes it possible to combine a
DF that depends only on classical integrals with orbits that respect
non-classical integrals. With such a combination, Schwarzschild's orbits are
used only to represent the difference between the true galaxy DF and an
approximating classical DF. The new method is used to construct a dynamical
model of the inner Galaxy. The model is based on an orbit library that contains
22168 regular orbits. The model aims to reproduce the three-dimensional mass
density of Binney, Gerhard & Spergel (1997), which was obtained through
deprojection of the COBE surface photometry, and to reproduce the observed
kinematics in three windows - namely Baade's Window and two off-axis fields.
The model fits essentially all the available data within the innermost 3 kpc.
The axis ratio and the morphology of the projected density contours of the COBE
bar are recovered to good accuracy within corotation. The kinematic quantities
- the line-of-sight streaming velocity and velocity dispersion, as well as the
proper motions when available - are recovered, not merely for the fitted
fields, but also for three new fields. The dynamical model deviates most from
the input density close to the Galactic plane just outside corotation, where
the deprojection of the surface photometry is suspect. The dynamical model does
not reproduce the kinematics at the most distant window, where disk
contamination may be severe.Comment: 20 pages, 5 gif figures, 11 postscript figures, submitted to MNRAS.
Zipped postscript available at
http://www-thphys.physics.ox.ac.uk/users/RalfHafner/paper.ps.g

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