Abstract:
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.

Abstract:
It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere, the logarithmic cusp slope 'g' of the tracers must be given exactly by g=2b where b is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the singular isothermal sphere, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging velocity dispersion also traces the behavior of the potential. The implication of our theorem on projected quantities is also discussed. We argue that our theorem should be understood as a warning against interpreting results based on simplifying assumptions such as isotropy and spherical symmetry.

Abstract:
The majority of Milky Way extrasolar planets likely reside within a few kpc of the Galactic centre. The Galactic tidal forces acting on planets scale inversely with radius in the Galaxy and so are much greater in the inner Galaxy than in the Solar neighbourhood. Within a range of 3.5 to 10 kpc, the vertical tide from the Galactic disc is predominant. Interior to 3.5 kpc, the effects of the Galactic bulge cannot be neglected and the in-plane tidal components are as important as the vertical ones. Here, we quantify the orbital changes induced by these tides. We find that the greatest perturbations occur when the planetary orbit is severely misaligned to the parent star's orbit. When both planes are perpendicular, the eccentricity of the planet is driven to unity, although the semimajor axis is secularly unaffected. When both planes are coincident, the effect from Galactic tides is minimized, but remains non-zero. In these cases, we provide estimates for the survival times, as well as the minimum baseline eccentricity variation for all Milky Way exoplanets as a function of Galactic parameters. Inclinations similar to the Solar System's (about 60 degrees) can easily cause eccentric Neptunes (at about 30 AU) around host stars deep within the Galactic bulge (within 50 pc) to experience eccentricity variations of several tenths, and cause the exoplanets with the widest-known separations (at about 1000 AU) to experience similar variations in the Galactic disc. These variations occur on timescales of a few Gyr, a fraction of a typical main sequence lifetime.

Abstract:
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the equations of motion of the unaveraged perturbed two-body problem in terms of planetary orbital elements by using a generalized form of Gauss' equations. We consider a varied set of position and velocity-dependent perturbations, and also derive relevant specific cases of the equations: when they are averaged over fast variables (the "adiabatic" approximation), and in the prograde and retrograde planar cases. In each instance, we delineate the properties of the equations. As brief demonstrations of potential applications, we consider the effect of Galactic tides. We measure the effect on the widest-known exoplanet orbit, Sedna-like objects, and distant scattered disk objects, particularly with regard to where the adiabatic approximation breaks down. The Mathematica code which can help derive the equations is freely available upon request.

Abstract:
The sky distribution of cosmic rays with energies above the 'GZK cutoff' holds important clues to their origin. The AGASA data, although consistent with isotropy, shows evidence for small-angle clustering, and it has been argued that such clusters are aligned with BL Lacertae objects, implicating these as sources. It has also been suggested that clusters can arise if the cosmic rays come from the decays of very massive relic particles in the Galactic halo, due to the expected clumping of cold dark matter. We examine these claims and show that both are in fact not justified.

Abstract:
This paper reports the star count predictions of warped and flaring models of the outer Milky Way disk. These have been suggested as possible locations of the lenses responsible for the microlensing events towards the Large Magellanic Cloud (LMC). Three such models are investigated in detail and the theoretical predictions are confronted with {\it Hubble Space Telescope} (HST) star count data in 7 low latitude fields ($30^\circ < | b| < 40^\circ$). If the warped and flaring disk population has the same characteristics as disk stars in the solar neighbourhood, then the models can be unambiguously ruled out. Metallicity gradients are well-known in disk galaxies and may cause the outer disk population to differ in colors and luminosity from that locally. This effect is studied using a simple ansatz for the variation in the color-magnitude relation with position and while it is shown to lead to better agreement with the star counts, upper limits on the contribution of the warped and flaring disk to the optical depth are still below the value measured towards the LMC. Only if the warp is very asymmetric or if the luminosity function changes strongly with Galactocentric radius can the models be made consistent with the starcounts.

Abstract:
We present self-consistent triaxial stellar systems that have analytic distribution functions (DFs) expressed in terms of the actions. These provide triaxial density profiles with cores or cusps at the centre. They are the first self-consistent triaxial models with analytic DFs suitable for modelling giant ellipticals and dark haloes. Specifically, we study triaxial models that reproduce the Hernquist profile from Williams & Evans (2015), as well as flattened isochrones of the form proposed by Binney (2014). We explore the kinematics and orbital structure of these models in some detail. The models typically become more radially anisotropic on moving outwards, have velocity ellipsoids aligned in Cartesian coordinates in the centre and aligned in spherical polar coordinates in the outer parts. In projection, the ellipticity of the isophotes and the position angle of the major axis of our models generally changes with radius. So, a natural application is to elliptical galaxies that exhibit isophote twisting. As triaxial St\"ackel models do not show isophote twists, our DFs are the first to generate mass density distributions that do exhibit this phenomenon, typically with a gradient of $\approx 10^\circ$/effective radius, which is comparable to the data. Triaxiality is a natural consequence of models that are susceptible to the radial orbit instability. We show how a family of spherical models with anisotropy profiles that transition from isotropic at the centre to radially anisotropic becomes unstable when the outer anisotropy is made sufficiently radial. Models with a larger outer anisotropy can be constructed but are found to be triaxial. We argue that the onset of the radial orbit instability can be identified with the transition point when adiabatic relaxation yields strongly triaxial rather than weakly spherical endpoints.

Abstract:
This paper pioneers the use of neural networks to provide a fast and automatic way to classify lightcurves in massive photometric datasets. As an example, we provide a working neural network that can distinguish microlensing lightcurves from other forms of variability, such as eruptive, pulsating, cataclysmic and eclipsing variable stars. The network has five input neurons, a hidden layer of five neurons and one output neuron. The five input variables for the network are extracted by spectral analysis from the lightcurve datapoints and are optimised for the identification of a single, symmetric, microlensing bump. The output of the network is the posterior probability of microlensing. The committee of neural networks successfully passes tests on noisy data taken by the MACHO collaboration. When used to process 5000 lightcurves on a typical tile towards the bulge, the network cleanly identifies the single microlensing event. When fed with a sub-sample of 36 lightcurves identified by the MACHO collaboration as microlensing, the network corroborates this verdict in the case of 27 events, but classifies the remaining 9 events as other forms of variability. For some of these discrepant events, it looks as though there are secondary bumps or the bump is noisy or not properly contained. Neural networks naturally allow for the possibility of novelty detection -- that is, new or unexpected phenomena which we may want to follow up. The advantages of neural networks for microlensing rate calculations, as well as the future developments of massive variability surveys, are both briefly discussed.

Abstract:
We have used the publicly released Dark Energy Survey data to hunt for new satellites of the Milky Way in the Southern hemisphere. Our search yielded a large number of promising candidates. In this paper, we announce the discovery of 9 new unambiguous ultra-faint objects, whose authenticity can be established with the DES data alone. Based on the morphological properties, three of the new satellites are dwarf galaxies, one of which is located at the very outskirts of the Milky Way, at a distance of 380 kpc. The remaining 6 objects have sizes and luminosities comparable to the Segue~1 satellite and can not be classified straightforwardly without follow-up spectroscopic observations. The satellites we have discovered cluster around the LMC and the SMC. We show that such spatial distribution is unlikely under the assumption of isotropy, and, therefore, conclude that at least some of the new satellites must have been associated with the Magellanic Clouds in the past.

Abstract:
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.