Multiscale probability mapping: groups, clusters and an algorithmic search for filaments in SDSS
We have developed a multiscale structure identification algorithm for the detection of overdensities in galaxy data that identifies structures having radii within a user-defined range. Our "multiscale probability mapping" technique combines density estimation with a shape statistic to identify local peaks in the density field. This technique takes advantage of a user-defined range of scale sizes, which are used in constructing a coarse-grained map of the underlying fine-grained galaxy distribution, from which overdense structures are then identified. In this study we have compiled a catalogue of groups and clusters at 0.025 < z < 0.24 based on the Sloan Digital Sky Survey, Data Release 7, quantifying their significance and comparing with other catalogues. Most measured velocity dispersions for these structures lie between 50 and 400 km/s. A clear trend of increasing velocity dispersion with radius from 0.2 to 1 Mpc/h is detected, confirming the lack of a sharp division between groups and clusters. A method for quantifying elongation is also developed to measure the elongation of group and cluster environments. By using our group and cluster catalogue as a coarse-grained representation of the galaxy distribution for structure sizes of <~ 1 Mpc/h, we identify 53 filaments (from an algorithmically-derived set of 100 candidates) as elongated unions of groups and clusters at 0.025 < z < 0.13. These filaments have morphologies that are consistent with previous samples studied.