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Register a new userGravitational potential of a homogeneous circular torus: new approach
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The integral expression for gravitational potential of a homogeneous circular torus composed of infinitely thin rings is obtained. Approximate expressions for torus potential in the outer and inner regions are found. In the outer region a torus potential is shown to be approximately equal to that of an infinitely thin ring of the same mass; it is valid up to the surface of the torus. It is shown in a first approximation, that the inner potential of the torus (inside a torus body) is a quadratic function of coordinates. The method of sewing together the inner and outer potentials is proposed. This method provided a continuous approximate solution for the potential and its derivatives, working throughout the region.
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We present the discovery of another Odd Radio Circle (ORC) with the Australian Square Kilometre Array Pathfinder (ASKAP) at 944 MHz. The observed radio ring, ORC J0102-2450, has a diameter of ~70 arcsec or 300 kpc, if associated with the central elliptical galaxy DES J010224.33-245039.5 (z ~ 0.27). Considering the overall radio morphology (circular ring and core) and lack of ring emission at non-radio wavelengths, we investigate if ORC J0102-2450 could be the relic lobe of a giant radio galaxy seen end-on or the result of a giant blast wave. We also explore possible interaction scenarios, for example, with the companion galaxy, DES J010226.15-245104.9, located in or projected onto the south-eastern part of the ring. We encourage the search for further ORCs in radio surveys to study their properties and origin.
Newtonian gravitational potential sourced by a homogeneous circular ring in arbitrary dimensional Euclidean space takes a simple form if the spatial dimension is even. In contrast, if the spatial dimension is odd, it is given in a form that includes complete elliptic integrals. In this paper, we analyze the dynamics of a freely falling massive particle in its Newtonian potential. Focusing on circular orbits on the symmetric plane where the ring is placed, we observe that they are unstable in 4D space and above, while they are stable in 3D space. The sequence of stable circular orbits disappears at $1.6095cdots$ times the radius of the ring, which corresponds to the innermost stable circular orbit (ISCO). On the axis of symmetry of the ring, there are no circular orbits in 3D space but more than in 4D space. In particular, the circular orbits are stable between the ISCO and infinity in 4D space and between the ISCO and the outermost stable circular orbit in 5D space. There exist no stable circular orbits in 6D space and above.
Efficient expansions of the gravitational field of (dark) haloes have two main uses in the modelling of galaxies: first, they provide a compact representation of numerically-constructed (or real) cosmological haloes, incorporating the effects of triaxiality, lopsidedness or other distortion. Secondly, they provide the basis functions for self-consistent field expansion algorithms used in the evolution of $N$-body systems. We present a new family of biorthogonal potential-density pairs constructed using the Hankel transform of the Laguerre polynomials. The lowest-order density basis functions are double-power-law profiles cusped like $rho sim r^{-2 + 1/alpha}$ at small radii with asymptotic density fall-off like $rho sim r^{-3 -1/(2alpha)}$. Here, $alpha$ is a parameter satisfying $alpha ge 1/2$. The family therefore spans the range of inner density cusps found in numerical simulations, but has much shallower -- and hence more realistic -- outer slopes than the corresponding members of the only previously-known family deduced by Zhao (1996) and exemplified by Hernquist & Ostriker (1992). When $alpha =1$, the lowest-order density profile has an inner density cusp of $rho sim r^{-1}$ and an outer density slope of $rho sim r^{-3.5}$, similar to the famous Navarro, Frenk & White (1997) model. For this reason, we demonstrate that our new expansion provides a more accurate representation of flattened NFW haloes than the competing Hernquist-Ostriker expansion. We utilize our new expansion by analysing a suite of numerically-constructed haloes and providing the distributions of the expansion coefficients.
The gravitational properties of a torus are investigated. It is shown that a torus can be formed from test particles orbiting in the gravitational field of a central mass. In this case, a toroidal distribution is achieved because of the significant spread of inclinations and eccentricities of the orbits. To investigate the self-gravity of the torus we consider the $N$-body problem for a torus located in the gravitational field of a central mass. It is shown that in the equilibrium state the cross-section of the torus is oval with a Gaussian density distribution. The dependence of the obscuring efficiency on torus inclination is found.
We present a proof of concept of a new galaxy group finder method, Markov graph Clustering (MCL; Van Dongen 2000) that naturally handles probabilistic linking criteria. We introduce a new figure of merit, the variation of information statistic (VI; Meila 2003), used to optimise the free parameter(s) of the MCL algorithm. We explain that the common Friends-of-Friends (FoF) method is a subset of MCL. We test MCL in real space on a realistic mock galaxy catalogue constructed from a N-body simulation using the GALFORM model. With a fixed linking length FoF produces the best group catalogues as quantified by the VI statistic. By making the linking length sensitive to the local galaxy density, the quality of the FoF and MCL group catalogues improve significantly, with MCL being preferred over FoF due to a smaller VI value. The MCL group catalogue recovers accurately the underlying halo multiplicity function at all multiplicities. MCL provides better and more consistent group purity and halo completeness values at all multiplicities than FoF. As MCL allows for probabilistic pairwise connections, it is a promising algorithm to find galaxy groups in photometric surveys.
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