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Register a new userA new approach to finding galaxy groups using Markov Clustering
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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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We explore the clustering of galaxy groups in the Galaxy and Mass Assembly (GAMA) survey to investigate the dependence of group bias and profile on separation scale and group mass. Due to the inherent uncertainty in estimating the group selection function, and hence the group auto-correlation function, we instead measure the projected galaxy--group cross-correlation function. We find that the group profile has a strong dependence on scale and group mass on scales $r_bot lesssim 1 h^{-1} mathrm{Mpc}$. We also find evidence that the most massive groups live in extended, overdense, structures. In the first application of marked clustering statistics to groups, we find that group-mass marked clustering peaks on scales comparable to the typical group radius of $r_bot approx 0.5 h^{-1} mathrm{Mpc}$. While massive galaxies are associated with massive groups, the marked statistics show no indication of galaxy mass segregation within groups. We show similar results from the IllustrisTNG simulations and the L-Galaxies model, although L-Galaxies shows an enhanced bias and galaxy mass dependence on small scales.
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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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